Here I'm answering some questions about the Run and Hit power-up from DF11, p. 12.
So I get +2 to damage?
Not exactly. You get +2 to Striking ST, which is usually +2 to cut and +1 to thrust. Important note: For the sake of simplicity I'll be running this as +2 swing and +1 thrust.* You also only get this if your previous turn was a Move. If you attacked during that move, you took Move and Attack and not Move. So no, you can't basically keep running around full-speed claiming a Run and Hit damage bonus every turn. If you want +2 Striking ST, you must do the following:
Turn 1: Move.
Turn 2: Move and Attack.
Can I Hit & Run?
Yes. It's a Move and Attack, and you can attack at any point along the move.
Do I still get the +2 to Striking ST if I Hit & Run?
Yes, if the previous turn was spent doing a Move.
Can I defend normally with my off-hand weapon?
Yes, but you cannot Retreat and you're at -2 to any DX-based roll, so Acrobatic Dodge might not work so well.
Did I miss any FAQs not answered by the wording of DF11, p. 12 or in DFD: Swashbucklers, p. 22.
* You will not get to "choose" to raise ST instead if you're at some breakpoint. Game is slow enough.