1. Replay on Penalties is a very tricky question. For example, can a defense throw the challenge flag when they give up a big play and claim that there was offensive line holding? Are missed pick plays reviewable? Can the defense throw the red flag and ask the refs to look for offensive PI? What level of holding and offensive PI is going to be called in super slow motion from multiple angles? People might say limit it to the obvious ones, but there's always a gradient where obvious meets less obvious. For Defensive PI, the recent missed call was obvious, but there are lots that are not. And everything looks very different in slow motion.
I suppose you could put some parameters on it, like if there is visible contact between defense and receiver, when the ref is ruling catch or incomplete, they also have to acknowledge to each other why the visible contact was not Offensive or Defensive PI. Not announcing every time, but like how on the sidelines they look to each other for feet and possession. Like "Catch, defender initiated contact, no O-PI" or "Catch with mutual contact, no PI" or "Incomplete, contact simultaneous to ball" or "Incomplete, defender looked to the ball and tried to play the ball." Then, there could be a specific thing that was challenged, like if the ref said "Incomplete, lots of contact, but defender looked at the ball and tried to play it" you could throw the flag and say "no he didn't," and if the replay showed he never turned his head to look, it would be DPI. Or in the Saints' case, it would have been "Incomplete, bang-bang contact" and the Saints could have challenged and said "contact was way early" and would have been proven right. Also not a bad idea to go with Bill Simmons' suggestion that PI penalties are watched in real-time, no slow motion.
2. I'm fine with OT the way it is. Someone has to win sometime. If you can't win in regulation, you're already on thin ice, and if you can't get a stop, that's tough. I hate the college system, honestly. The current NFL system is better than pure sudden death. It would be interesting to just say OT is a full 15 minutes, and just leave it at that, then say the 6th quarter gets the current OT rules.