For a transfer applicant, is it wise to ask the university applied to, not to contact my current one?
I don't think it is wise. Such things would probably do more harm to your case. I see no reason for C to be "repercussive" to students trying to transfer. I've heard about particular professors to act that way, but never about institutions. In any case, their repercussions towards you are clearly an issue and should be addressed. However, this has nothing to do with the institution A, which will follow its procedures. If you issued such request to A, they would probably think that you have something to hide.

As for C, you should clearly transfer to another institution if the claims you have laid out are true. Don't fret about what they will think. It is your education and your life and you are free to make decisions which suit you best.