Pedro's answers to your questionsPedro's answers to your questions
I've been around this site for almost 3 years now. I've been in a math undergraduate program for that time, too. Being the most active user in the the (official?) chat room (with around 90 thousand messages so far) it is highly probable you'll find me there. I'd like to believe this is also accompanied by quality in my answers and posts.
I generally do some work related to changing titles, tags, adding TeX, and guiding the OP to either producing a better post or a solution to his/her problem. I comment quite a lot, sometimes for the better, sometimes for the worse. I have had my quarrels with some users, and quarrel with some in chat, but this happens in a more facetious manner. I have probably been suspended from chat a few times.
Ideally, I would want MSE to make users understand there's a certain "quality of user" the community is expecting: show your work, explain your ideas, code your TeX, choose appropriate titles, engage in discussion in comments, welcome criticism, criticize.
Regarding closing issues, I usually close "closable" questions. This is sometimes seen as a bad thing, but personally, it's the best way for people to improve their post quality.