Fold Equity Hypothetical

You're holding 32 and the pot has reached $100. The river comes and you missed your str8 draw. You missed your flush draw, too. You got the nut low with 3 high, but sadly, this isn't razz. This is no limit hold'em and all the cards are out there. For the sake of simplicity, we'll assume your lone opponent can beat 3 high and you're NOT chopping if it gets to showdown. You decide to make a pot sized $100 bet to TRY to take down the pot since that's the only way you can win.

Question #1
What % of the time does your opponent need to fold for this to be a BREAK-EVEN play?

Question #2
Hypothetically, if the villain had 3rd pair, 9's on a board that had a King and a Ten, what % of the time does the hero need to be bluffing with air (no pair) like we actually are in this example so that villain CALLING your pot sized $100 bet is a BREAK-EVEN play for him?

Question #3
What % of the time does your opponent need to fold for this to be a BREAK-EVEN play if hero bets $50 (1/2) pot instead of $100 (full pot)?

Question #4
Hypothetically, if the villain had 3rd pair, 9's on a board that had a King and a Ten, what % of the time does the hero need to be bluffing with air (no pair) like we actually are in this example so that villain CALLING your 1/2 sized $50 bet is a BREAK-EVEN play for him?