Can I transform a token copy of a double-faced card?
No, you cannot transform a token of Jace, Vryn&#39;s Prodigy this way.

110.5g A token that has left the battlefield can’t move to another zone or come back onto the battlefield. If such a token would change zones, it remains in its current zone instead. It ceases to exist the next time state-based actions are checked; see rule 704.

So any effect that exiles a token and then brings it back will fail to bring it back, and it will cease to exist next time state-based actions are checked.
Note that you cannot transform any token that is copying a double-faced card; but for a different reason. If you have a token copy of Delver of Secrets, and try to transform it, it will also fail.

701.27a To transform a permanent, turn it over so that its other face is up. Only permanents represented by double-faced cards can transform.
110.5e A token is subject to anything that affects permanents in general or that affects the token’s card type or subtype. A token isn’t a card (even if represented by a card that has a Magic back or that came from a Magic booster pack).