I assume when the ROC denies the unequal treaties after taking down the Qing the European powers will realize how big a threat China will become. With the Great War seemingly avoided (maybe) they might find solace in a bigger enemy to unite against, as the European Monarchies will work long and hard to entrap and limit the ROC's influence before they become Asia's, possibly the worlds dominant power.
Depends on the specific treaties.
Treaties such as the Treaty of Tianjin, which allows for extraterritoriality, are likely to be abandoned unilaterally by the ROC. However, specific terms, such as allowing for foreign trade, are almost certainly going to be maintained. The permitting of Christianity itself would likely be allowed as well, seeing that Sun and other prominent figures are Christian.
Foreigners themselves would likely have to live and behave under ROC law, but seeing that Taiwan itself is a largely "Modern" nation, it is likely that such laws would be reasonable. That said, it might piss some people off to lose certain diplomatic immunities.
But a big stickler is going to be the opium trade, which was legalized in the Treaty of Tianjin.
Yeah, the ROC is going to crack down on that. Hard. Of course, the reaction of each country would likely depend on who's doing the importing.
America? Yeah, I don't think they're doing is going to bother them that much. But Britain, the people who were responsible for opium being a problem in the first place? Oh boy are there going to be some angry merchants.
Meanwhile, the Boxer Protocol, much of which is largely expired by 1911, would have terms such as the Legation Quarter stripped of their extraterritoriality (though this would likely be due to everyone getting the Hell out if the ROC gets to Beijing). However, the consolation would be the creation of an "Embassy Row" in Nanjing (the presumed capital), with the usual provisions that a modern embassy enjoys (basically being considered territory of the embassy's owners).
In general, I imagine the ROC would be more than happy to open their ports to foreign trade. Free trade is kind of the status quo in Taiwan already, and China can quickly outproduce many of the European countries in certain industries such as steel. I'll have to look for the data, but I remember reading that Taiwan today produces a similar amount of steel to Britain about a hundred years ago.
Tariffs will likely need to be renegotiated, but I imagine that would be one of the less contentious issues and could be negotiated in due time.
Couple that with an effective monopoly on several products (vehicles, computers, radios, medicine, tea, and the like), and I believe that opening up even more ports would benefit
China more than the Europeans.
If I'm being honest, the Europeans and Americans don't really have that much that China would want, besides raw goods (iron, oil, etc) that the Chinese haven't been able to extract in decent amounts or can't extract.
Manufactured goods? Well, I guess they be sold as antiques in Taiwan.
Guns? Museum pieces. I heard Colonel Chen is likely to be the newest donor to Taipei's museums.
Now, how would countries react to the ROC's intention to renegotiate or abandon several of the Unequal Treaties? It would likely depend on the nation.
The United States, for example, seeing a revolutionary liberal nation that is led by people who
really like the United States and are one of their newest trade partners, might be more willing to renegotiate, as their possessions in the area largely consist of a few autonomous settlements and the legation they would likely have abandoned and would soon be replaced with an embassy in Nanjing. They may be more-willing to accept terms in exchange for trade. For that cost, it would be a decent price to pay for advances in technology, medicine, and modern goods, as well as a potential ally against the Japanese.
Of course, there will be people in the US who would raise a fuss over this, but that would likely be compensated with either shares in new companies or outright payment.
But I imagine that resistance to renegotiation is directly proportional to how much a country has to lose in what is an "Overnight Superpower." I started with America for example, since
I am American they have the least to lose.
But a country like Russia, who basically kicked China while it was down during the Taiping Rebellion to take Outer Manchuria in the 1858 Treaty of Aigun and the 1860 Convention of Peking? Well, Chinese people in our history's 1920s already declared it an Unequal Treaty, so it is likely that the ROC is going to want it back.
Not to mention that they would very much like foreign troops to get the hell off their land and for foreign warships to leave.
And unlike America, Russia has its troops out there in force. Okay, maybe not foreign warships after Japan exploded their Pacific fleet, but you get the idea.
That's going to be a problem, and that is
before we get to the fact that Tsar Nikolai II is actively plotting to try to snap off Xinjiang, Mongolia, and Manchuria while the Qing are busy (oddly enough, similar to how they got Outer Manchuria in 1858), as if he's playing Kaiserreich for Darkest Hour (when there used to be decisions to do that if you were playing as Russia). While the ROC may be stretched out, Russia would be sending troops to the other side of Siberia, which will make supplying them and supporting them a hassle...
And that's assuming nobody sabotages the Trans-Siberian Railroad.
As for the "Big Three" (Germany, France, and Great Britain), I imagine that they are going to be unhappy that the Chinese would want the new concessions that they gained less than two decades ago. The ROC would obviously want them, and I imagine that the Big Three would want to ride out their leases for the next century.
These three are going to be a bigger hassle. While Russia is on the other side of Eurasia (with a rebuilding Pacific fleet and a Baltic fleet that is historically run by stupid people), and Japan is likely going to get their asses kicked if they try anything funny ever again, these three actually pose a decent threat.
Out of the three of them, Germany is likely (and ironically) the weakest. While the Kaiserliche Marine is formidable, they face a severe case of "On the Other Side of the Planet Syndrome." That said, they do have a decent amount of possessions in the Pacific that they can use as a jumping-off point, and the ROC doesn't really have that much amphibious warfare capacity on the grounds of the Marines ramming their makeshift landing craft into the shore of Guangzhou to land there.
Sure, they
could try to invade Eastern Papua, but that would take a literal year, so that might be less-than ideal.
France, in the meantime, is the second-strongest. Sure, the German Army is stronger on land and the Royal Navy is the strongest Navy on the planet, but France has French Indochina as a jumping-off point. While I'm sure that Agent Li and Agent Fong are probably coming up with some very funny plan to liberate Indochina, likely in the form of convincing "volunteers" to jump the border and go "General Sherman" while rebel troops who happen to be suspiciously well-armed start a rebellion, China doesn't really have the force projection outside of Zhanjiang.
Could the ROC take it? Sure, it's literally on their border and they could likely take it over in a week.
But a land war in Indochina would likely ensue.
Last but not least is the British Empire, who in addition to having the Royal Navy, have a massive empire around the world that could boycott China. Which, while they don't really
need the British for trade, I imagine Sun would almost certainly like to be on good terms with them.
That said, they have the most concessions out of almost any country, and I'd imagine that the ROC would want it back. All of them.
How this would unfold, well, we'll cross that bridge when we get there. But I imagine that the ROC doesn't want to go toe-to-toe with the Royal Navy for the foreseeable future, at least until they can build more than a dozen ships.
As for your last point about the Great War likely being avoided, it is likely that the Conference of Copenhagen will likely be held to prevent such a conflict. While I doubt that Europe as a whole would ally together (for many, many reasons), I do believe that the European powers would see the ROC as a threat to their colonial possessions and actively try to not weaken each other. While they would like to carve the country up into pieces, I imagine that they wouldn't be that effective in practice.
That said, they likely see China as a threat to their colonial empires. Here is a country with a massive population, an exponentially-rocketing industrial base, as well as the nation serving as a symbol of anti-Imperialism (and more importantly, anti-Monarchism).
Here is a country that basically spits on every justification of colonialism (from rights, to technology, to even religion), and they have every reason to fear that their own revolution could happen in their colonial possessions, and that it may come from China itself. Or at least the revolutionaries who flock to the ROC once the Chinese Republicans win.
However, it will likely not be China vs. the World. Not everyone is going to see China as a threat. In fact, many may see it as an ally, a potential trading partner, and a means of modernization.
I've already mentioned the United States likely being very favorable to the ROC, and I should add that is also partially due to their one colonial possession, the Philippines, being a place that they planned to get out of sooner or later, after a transition period. Having an China that is modernized and very friendly to them will, in all likelihood, actually speed up decolonization in the Philippines.
Meanwhile, the Ottomans are likely to have little reason to want to screw over China. Why would they see China as a threat when they don't have any possessions or colonies in Asia? If anything, the Chinese may be seen as a model for the Ottomans to work with, a trading partner and a seller of machinery and weapons, and a willing partner in modernization of their society as a whole.
The same could be said of the Italians, Belgians, and the Austro-Hungarians. All three nations have only legations in Tianjin that they'll probably vacate when the Revolutionaries close in on the area. But at the same time, they also don't have concessions that the Chinese would want back, which makes them potential trade partners. Oh, and while Belgium does have the Congo (and I'm sure the ROC would like to liberate that, like, 20 years down the road), I don't think Belgium is going to be worried about China trying to start a revolution there.
Portugal, for their part, is going to be a bit more iffy, on account of Macau. Sure, they also had their own revolution the previous year (and I don't think that they would have any real means to respond), but I imagine that the ROC would likely try to negotiate for the island back.
Which, given their stronger position on the mainland, likely gives them a good amount of leverage, even if Britain backs Portugal. That said, the ROC would probably just try to buy the island from them with a trade deal, medical support, or currency.
So in short, the Uneven Treaties will likely be undone, but it depends on the specific terms of each treaty. Extraterritoriality, stationing of troops, opium, and having Chinese land are likely to be rejected, but the ROC would likely be open to free trade, renegotiated tariffs, as well as Christianity.
Maybe not the Evangelicals, if they get kinda weird about it, but for the most part even they should be fine, I imagine.
But yes, I imagine that with China being a quickly-rising power, countries and peoples will have different reactions.
Colonial powers in Asia would see them as a threat, while non-colonial powers would see them as a trading partner, ally, or means of modernization.
As for colonized or subjugated peoples, whether they be Africans, Malays, Indians, Koreans, Poles, Ukrainians, Finns, or Baltic peoples, China may be seen as a symbol of independence and anti-imperialism.
But first, China will have to rebuild to get there, and that may take the better part of a decade.