Invisible Tentacles triggers before the attack even starts. It would stop Shiftry RR's Conform, provided you have the same number of cards before the attack starts. Of course, if the opponent has 1 more than you, and then discards for attacking, by then you would have the same number of cards, so Conform would work.
In regards to Yanmega Prime...eh. I'll need to consult the set FAQ.
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There's nothing regarding it yet, so there's no official answer. I personally would say no, because at the time you're announcing the attack, the requirements have been met. But don't take my word for it.