Quick and Easy Questions (please read the OP)

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Are moves that temporarily allow the use of powers,  even if you don't have them allowed?

No.

As far as I know, the only exception is mimic.

Mimic – 2800 OM

A tactical and versatile ability, Mimic allows you to copy any powers or moves you've seen (or read with Insight) for up to an hour afterwards in-character. You must witness this in-person; watching someone use a move on a screen, for example, will not work. To use a Super Move you have copied, you must also pay the SP cost for it, and to copy things permanently you must buy them with OM (i.e. you have to buy the move yourself if you want to keep it in all circumstances). Bear in mind that you will not copy the target's stats - the move's effectiveness will depend on your own stats - and you will be somewhat less skilled than if you had the ability or move yourself.