It seems unlikely that gangs would be fighting in space itself, they may fight inside of a space station or habitable dome, but few will be doing space walks, not enough for there to have developed common fighting style for it. I imagine the majority of fights will be 'indoors', because why would a gang member or laymen want, possess authority for, and have equipment and gear for being in space?
Likewise there is little reason for a military to every fight in space. Drones will be more viable in 100 different ways to trying to make a human with full support system just to give him a gun. Close quarter fights inside of your space ship, trying to take over the command room for instance, may occur, but not fights in space. All the fighting with humans will be done within a controlled enviroment that everyone is fighting over controlling.
Fights in EVA gear in space will still occur on occasions, humans find opportunities to fight always, but they will be random incidents, not organized battles. I would say they would be clumsy pathetic things, because no one has developed techniques, weapons, or EVA suits designed for it. The suits will not be designed to protect against bullets and will be just as easily pierced by them. However, bullets won't fire in space, and there is no reason to design a 'space gun' for space battles since, as I said, they will not be standard or desirable way to fight. Thus I would see a space fight either being a clumsy melee fight to try to pierce the others suit or damage it before they do the same to you first, or possible at slightly longer ranges using regular tools as jerryrigged weapons, Imagine using the equivalent of a gigantic staple gun as a long range weapon to pierce someone's suit.
Of course one whole in someone's suit won't kill them. Suits will have plenty of redundancy. They will not be deigned well for combat, but they will have enough redundancy that even if damaged you still have time to get to an airlock. In fact severing your opponents teather to the space station may be a more viable weapon, without that they will soon find themselves floating off into space.
Most of the battle, as I said, would be in enclosed spaces, fighting over controlling whatever habitat everyone is in. These will be roughly similar to standard close-quarters inner city warfare of today, with some possible exceptions. The problem is it's hard to say the exceptions without knowing more about the technology of your world.
1) Gravity, or lack of it, will cause interesting conflicts. Are they using artificial gravity, centrifugal force, or actual gravity of an atmosphereless moon to hold them to the ground? If their in zero G everyone will have to learn to fight in 3 dimensions, which is not easy to learn. The inability to simply change your direction once floating will also make team formations harder. Weapons will likely not be your standard guns, since the kick with a gun would be so large as to throw off your trajectory and movement when fired. Perhaps they will use weapons designed to fire far smaller rounds at high speed, or a system to counteract the kick of the gun by releasing some equal-opposite force behind it.
2) Depending on how your habitat is enclosed risks of damaging the habitat may exist. Larger weapons, anything more powerful then a grenade, may be thrown out as the risk of doing significant harm to the delicate systems keeping the habitat in place are so great. This would be a great reason of justifying a large infantry if you wish it, claiming all the powerful weapons can't be used in the enviroment for fear of the harm their do, so we resort to lots of small arms instead.
I would also say that there would totally be zero G combat sports, and they will be amusing to watch. In fact there would likely be many different types of combat sports. Some may put you in a small dome and say "fight it out". In theses cases both sides would 'launch' at each other until they collide, then it would turn into a rather boring grappling match as the bounce around the walls (then again, some find grappling MMA fights to be interesting lol). Other sports may impose other rules, such as a form of fencing where registering hits with foils which are sufficient to Peirce a space suit count as damage; which would result in a sport that is more about acrobatically flinging yourself through a 3D maze of platforms to manure around your opponent into a position to land a strike. Many other zero g sports could exist, in fact if it wasn't too much of 'idea generation' I would post a question just asking for all the different zero G sports that might exist.