Rules

Does "I Break the Rules" let me play a second Piece on my turn?  
Yes!

Does "I Break the Rules" let me put the piece over here on the floor? It says anywhere. 
We like the cut of your jib! But no. It must still go adjacent to another Piece already in play. Either orthogonal, diagonal, or stacked.

I played "You Lost Your Seat" whose turn is it now?
You finish your turn in your new seat then play continues to your new neighbor.

I played "You Lost Your Seat" what happens to the Win Conditions?
Win Conditions stay on the table with your Holdings.

I played "You Lost Your Seat" while "It's a Co-Op Game" was in play, does my team change?
No. You have a new seat and a new hand but you are still you. Which means all teams remain the same.

Can "I Check the Rule Book" be used to get a discarded Event/Board State/Win Condition?
Nope, only Rule cards.