"Can I use the bathroom?"
I disagree on that. トイレをかしてください sounds rather rude, and I have yet to hear any native speaker ask like that. ください is used to form orders not request. Yes in a polite way, but using it implies you are not expecting a negative answer. The form in ていいですか seems way more suited to me, as we're asking for a request.
I was going to ask this as well. When Looked in my dictionary, I found what look like related entries:
貸す, 藉す [かす]: (P, v5s, vt) to lend, to loan, to rent out, to hire out
仮す [かす]: (v5s, vt) to grant, to allow, to forgive
Does anyone know if 仮す could also be used?