If Parallel Universe gets canceled does it stay in my hand or does it get discarded?

The problem is that it is not the Parallel Universe card the one that is being cancelled, it's Action: is. On an Event card, the distinction is negligible because Event cards are put on the discard pile after they are played, regardless of it's effect working or not. Parallel Universe is a Support card, so if it's "put me in play" written Action gets cancelled, then it is not put into play by it, and remains where it was, in your hand. This applies to both Character and Support Cards with "put me into play" Actions.

So after reading the new FAQ on Dreamland Fanatic it seems also Parallel Universe gets discarded.

Right, they finally choose the option to have a card wasted ...