Consequentialism covers all morality that's based in the outcomes of actions. Utilitarianism is the kind of consequentialism focused on maximizing happiness. Deontology is rules-based morality.

I think hypotheticals can be useful as long as the example actually is universifiable. In the trolley problem, the real question is "Is it okay to directly cause a bad thing to happen if it will prevent a worse thing (which you did not directly cause) from happening" which is IMO a worthwhile question to ask whose answer is applicable to many different scenarios. I think it's possible to misapply a hypothetical, since the scenarios might not actually be comparable, but if they are, I think we should apply our principles consistently, and having hypotheticals helps us do that.

Oh shit, I took it literally. I thought I was teaching philosophy but I guess I've just been murdering people this whole time.