For your first problem, I would say that the store means by the statement, "No shoes, no shirt, no service", that if you are lacking either shoes or a shirt, you will get no service.
For the second problem, I don't think you're using OR elimination correctly in line 8. (Nice formatting, by the way!). OR elimination works like this. If you want to use OR elimination, I would suggest you set up a p or not p, using the Law of the Excluded Middle (or, it's possible to derive it if your deduction system is robust enough with proofs by contradiction). The line 1 that you reference for the OR elimination isn't a disjunction!