broly, visible abs are great for the ego, but if you wanna gain some serious mass you gotta eat like it's your job, and the abs may go in hiding for a while. it's well worth it though after you've gained that mass and then cut back down to sheer rippedness. screw weighted chins, you gotta do weighted PULLUPS... they focus a lot more on the lats/upper back and won't tire out your bi's. a lot of the upper back interestingly enough consists of the trapezius muscle (traps), so you may want to hit shrugs really hard (DB work fine, i like to do some BB behind the back shrugs as well). btw, those shit little gyms can end up being your best friend... you get to train creatively with REAL free weights, not those pussy machines in newer gyms.
and also, i have no idea where you heard that pressing above the head is bad at your age, but it sounds completely ludicrous. if you want size, you can not neglect your shoulder girdle... make it strong, hit up DB military presses hard, now!