Game avatars, depending on the degree that we can alter them can be one of a few things. Commonly it is something the developer forced the player to pick and they really don’t care much. These players aren’t interesting to analyze so let’s forget about them for now. Other gamers will attempt to make their avatar exactly like them in real life. Making an avatar a reflection of oneself can be more immersive, allowing the player to feel like they are the one in the story and can make interacting with others in a virtual world more exciting. Some gamers will make their avatar closer to who they want to be rather than who they are. These people are trying to represent themselves in a way that makes them feel like they have more power or that they should be more respected than they are.
Violence in video games is not an issue that needs to be discussed, any evidence that is brought up is either wrong (see columbine killer’s letter stating it was not their paintballing or gaming that drove them) or circumstantial (kids being mad because they lost or was it because they already had anger issues). Games use a lot of violence because it is the most obvious and easiest type of conflict to include in a story or experience. There are many games that have no or almost no violence that are beloved by fans.
I would like to say yes. Specifically I would like to see the results of Eddie’s Thesis which is studying the cognitive capacity after playing games. There is some research but all of it is under specific circumstances so I cannot make a blanket claim although the outlook does look good.