Heyo! John here to answer more setting questions:
In a character's biography, you make mention of a Broker School. What is it like? Does it differ greatly between corporations, or say, have a neutral party to balance things out between corporations?
Not sure what character bio you're talking about? But brokers do go through training of sorts. Given the profession is technically illegal, most brokers get training in related fields: lots of project management, production, military, legal spy agencies or CorpSec backgrounds. Once someone decides to break into the Broker game, they either have to be head-hunted by an agency or work their contacts (another vital broker skill) to get in the door. Once in the agency, they're put under strict supervision and given increasing responsibilities, to see how they handle the pressure. The better they do, the more permissions and freedoms their given. Eventually they're promoted from an associate to a full broker, and then they'll keep climbing that ladder (or get burnt along the way).
Secondly, what does the average war look like? Do countries still have standing armies, or focus more on hiring mercenaries? Are there any sort of mechs or exoskeletons in use?
The "wars" are so varied and convoluted it's hard to identify an average. Much like the modern world, most wars involve sudden hot flashpoints of conflict, and prolonged guerilla warfare and "peacekeeping". Most corporations that are big enough to have sovereign arcologies have CorpSec divisions dedicated to combat, though once they get pulled into something it's common to hire contractors to pad out the regiments. Since Corps are also usually part of a larger federation (the governments we have today), there's also the federal troops in the conflict, sort of like UN troops. Most developed countries still have standing armies, sometimes volunteer and sometimes with mandatory service terms. Just like the modern world the tech level can range dramatically from battered AKs to dropships full of combat droids.
There are PCVs (Personal Combat Vehicles) which are sort of between a mech, a motorcycle, and an armoured jeep. They're fast and mobile, heavily armed and armoured, and tend to hold a pilot and up to two passengers on the back, mainly used for breaking entrenched positions or for quickly assuming flanking positions. They also see use in policing efforts, with an officer in a PCV carrying his partner in a Power Mesh, using the benefits of both to chase down high-threat criminals.
The Power Meshes are an exoskeleton used to augment soldier strength. Battery life is still a problem, so they're usually reserved for the Heavy Weapons guy to help haul MGs and ammo.
The droid dropships are used by first world countries though the cost usually keeps them for use in those flashpoint encounters. The humanoid robots are fast and adept at navigating tight urban environments, and are controlled by a combination of AI and pilots that stay in the armoured dropship and broadcast commands. The majority of fighters are still human, though; either due to cost restrictions or because they need to serve a broader purpose. Not to mention powerful PMC unions... droids are seen as a useful complement to normal forces.
Finally, it would seem the Net Gain world, as a whole, is focused on a shadowy, sneaky style of life, operating in the dark. Might there be locations where this differs from the norm? Say, Istanbul/Constantinople, a city-state caught between old and new, where a difficult legal system of laws create an environment where the rules are far easier to break. Maybe an certain area in South America is so hotly disputed, it has become a constant battlefield, to the point where many corporations test out new equipment or whatnot here.
Very much so! Most of Net Gain focuses on activities in more developed areas, so it's quite sneaky, but the rules of engagement vary widely depending on where you are. Exactly as you suggest, certain hotspots get so turned over by the chaos that they just become a place to put your PMCs to work and test new toys, with the benefit of grabbing up some land and resources if you can hold onto it for long enough, not to mention whatever your PMCs are paid for the contract in the first place. These are very dangerous regions to operate in, as the usual etiquette tends to be thrown right out the window.
Etiquette is also very different in various countries. Most wealthy countries have a policy of capturing and trading operatives (or on occasion, hiring them!). Though if an operative causes significant "disruption of the peace" or starts taking lives, they are often executed with extreme prejudice... and if they do capture them then a long and tortuous "intel extraction" can be expected. Various other unspoken rules can pop up: Attacking employees, invading personal homes, using family members as bargaining chips or targets. Not that it doesn't happen, just that if that becomes public knowledge the loss of face is significant, and retribution will be more severe.
(Though to clarify, not all aspects of the setting will make it into the game, or only in limited fashion, depending on how fun it is.)