Most Helpful Guy
You've got a couple questions here that have VERY different answers.
First, based on your life situation, it sounds like you are better off not asking this guy out and staying focused on your schoolwork. This is primarily because you already know that doing so has had a positive effect on your life. Add to it the restrictive nature of your life's circumstances and the lying and hiding and avoidance of the truth you'd have to do to pursue him, and it just makes everything too complicated to be a reasonable option.
Second, if your just asking about looking desperate and girls asking guys out - heck yes they can and should! Most guys like a girl who can take charge and know what she wants. In fact, plenty of guys find it sexy and appealing, so long as the girl isn't emasculating about it (and even that can be sexy and fun at times). In this day and age, it is rarely seen as desperate. It only looks desperate if you approach it hesitantly or timidly as if you are unsure of yourself or don't know what you want.
Confidence is key, and even if you flame out, do so with your head held high, cause there are plenty of other fish in the sea and a guy who turns you down does so at his own loss.