Yes and yes. Tokens don't care if the pile they're on is empty (though the trashing token doesn't do much in that case).
The only exception to this is when using Seaway, which requires a card gain before moving the +Buy token.
Seaway doesn't have an "if you do" clause, though, so it would seem you can still move the +Buy to an empty pile; you just don't get to execute the first instruction on the card.
No. The first instruction is to "gain an action card costing up to $4". You are not allowed to select an empty pile for this instruction; just as you can't select an empty pile for Workshop.
Also, even if you were allowed to select an empty pile, you wouldn't move the token, because it says "move your +1 buy token to
its pile." "It" refers to the card you gained, as per the blue dog ruling, so if you didn't gain a card, there's no card for "it" to refer to. It would be like using Ironworks to select an empty pile, then trying to get the Ironworks bonus for the card that should have been in that pile. Not only can'y you select the empty pile, but even if you could, there's no card to give Ironworks the bonus.
*Edit* Similarly, I'm pretty sure that if you reveal Trader to the Seaway gain, or if it's on a Possession turn, that you don't get to move the token.