Newbie questions... What are the Darkspawn, really? If they come from another world, can we go there in turn and take the fight to them? Are they all like the one we fought? Can the people who've been affected by their power be healed?
Generally, if you have questions it'd be best to look up the sourcebooks, link's low on the frontpage, or failing that to wait until it comes up in-story.
That said, some
quick answers:
Darkspawn are beings, often humans but also animals or other things, corrupted by (or sometimes formed from) the Darkness, an aggregation of all hate, pain, despair, hunger, and similar bad juju in existence. The majority are animalistic (but still often cunning!) monsters with the sole goal of hurting people in a variety of ways. Closely related are the Mnemosyne, which are formed similarly but trade raw strength and numbers for not losing their intelligence and for more versatile magic, and often act as leaders for any dark cults and darkspawn around. Then there's also the Cataphractoi, which combine the worst of both worlds, but the only thing we're likely to need to know about them for now is that if we see one, we run.
Invading the Dark World is kind of sort of not even theoretically feasible or likely to accomplish anything. The Dark World is an alternate (un)reality completely dominated by and shaped out of the Darkness, leeching off the real world and all the aforementioned bad juju therein to sustain itself - including the kind of suffering and hate generated by any fight let alone major military campaign, and quite possible doesn't even have any end in the physical terms, only ever greater depths of all-consuming void. Not to mention that it's capital-D dangerous to the point where some argue that literally no reason is good enough to enter it, that even if a loved one is kidnapped there the best thing to do is to hope that they died quickly (unlikely) instead of even attempting a rescue.
In theory, it might be possible to starve it out of existence by removing all suffering and hate in the world, every single small iota of disappointment or annoyance, but good luck with that, especially without resorting to brainwashing or similarly self-defeating measures. Not even the Kingdom at it's height was likely to have any real shot at archieving that, and that was an utopian society backed by scores of benevolent demigod-saints and ruled by literal bhodisattvas of peace and understanding and goodness.
The best way to defeat the Darkness is to contain it, to cleanse the places where the Dark World intrudes on and leeches off of the real world - the Tainted Places we're voting on investigating right now - and to prevent any new ones from forming by stopping suffering and acts of cruelty - murder, rape, abuse, bullying, neglect, vandalism, fraud, etc. - and especially to stop the servants of the Darkness which usually have just such acts as their main purpose of existence.
The creatures of Darkness can take just about any form imaginable, each more horrific, disgusting, and/or insidiously seductive than the last.
Healing them is possible if done early enough, when the Darkness is still just in the process of infesting and corrupting them - the proper term is they are Darkened. Eventually though, there comes a point where the Darkness devours them from within and then steals and uses their corpse like a cheap sockpuppet - the Darkspawn proper and company. At this point, in canon PtH and almost guaranteed here as well, they're beyond saving. Best case the original person is simply dead, worst case death is still a mercy to whatever tortured scraps of them are still imprisoned inside the Darkspawn.