Regarding timing structure of paid abilities, the rulebook says once both players get a chance to use paid abilities and then someone passes that ends paid abilities. Does that mean active player goes then inactive player goes and they both respectively do any paid abilities they want, but if the inactive player does nothing that paid abilities close? Or does that mean active player goes, inactive player goes, then it's back to the active player and as soon as a player chooses not to use paid abilities after the first cycle through then the paid abilities window ends?
It's the latter. From the rulebook: "After both players have had at least one opportunity to act and a player declines to act, then the players cannot trigger more paid abilities, rez more cards, or score more agendas until the next opportunity to do so."
There seems to be some confusion over my earlier answer to question 1. I would like to apologize for any confusion it caused. I was interpreting "the active player goes" and "the inactive player goes" as abilities being triggered or cards being rezzed. I see now that it just means "were given the opportunity to act." With regards to your question, the former description is the correct one: if a player has the opportunity to act and declines to act (does nothing), then the 'window' closes unless the other player has not yet had the opportunity to act.