Slaughter Mariner City? Absolutely not. It's hard to convey scale, especially since I try to keep certain things vague to not hamstring myself about numbers in the future, but I promise you - They are nowhere near able to kill an entire city.
However, the Mariner Stadium is not all of Mariner City. It is a primarily civilian location, with little air defenses, which much of Stadium's culture and government is centered around. Phoenix Company could have feasibly overrun it had MPA forces not been in position to fight them off, inflicting a devastating morale blow to Stadium, as well as wreaking havoc on their civilian population and logistical capacity. They also took losses during that fight, and it's unlikely they'd be able to significantly threaten a major population center without significant build-up/outside investment.
Their air power tends to have a bit of variety, as the Nomads had quite the variety, with their HQ being an actual airship on which they journeyed around. However, Phoenix Company primarily uses the military-style helicopters that the Nomads favored for combat engagements, rather than more civilian craft, due to their primary source being defecting Nomad military personnel. You can assume they have some civilian and transport craft as well, though.
Setting up better communication? Depends. If, say, you set up a rival to MBC and started broadcasting your own news/entertainment on a large scale, they'd probably be pissed, but there isn't really a Mars-wide...economy, as we would think of it? Like, most of Mars doesn't have a unified currency, there's no stock market...etc. There are trade routes, traders, and whatnot, of course, but MBC is part of the corporate bloc/capitalist because, in their own states, the means of production are in the hands of the elite, who enforce a strict hierarchy on their workers, among other things - Their 'profit margins' largely come from their population, rather than from selling to yours. Their primary interaction through exports/imports isn't profit/the flow of actual money, it's the flow of materials and goods in exchange for other materials/goods/whatnot. The threat of blockading them isn't necessarily about a strict exchange of money that you're stopping, it's about halting that flow of materials into their state/economy, which in turn will force them to tighten their belts/start rationing/hurt any attempt at major expansion, causing internal economic instability and public unrest.
Now, a lot of where setting up better communication would hurt them is in terms of the information war. If MBC's dominance over the airwaves is broken, a lot of their immigration might dry up as Station/MPA territory becomes seen as a land of opportunity, which will start to deprive them of cheap labor over time, causing further instability as workers demand more pay/more rights. In turn, their current monopoly on spreading information being disrupted significantly would be a hard blow to their ability to project influence - But at the same time, they have a lot more experience and a lot more infrastructure than you at the moment, to say nothing of the benefit of inertia.