Yes, you show both passports. Your visa has a passport number on it, so they want to see the passport that corresponds with your visa. But then since that passport is no longer valid, they will put your entry stamp into the new passport.
You don't need to do anything besides check to make sure you got the correct stamp before you leave the airport. Continue to carry both passports for the remainder of your DTV and you shouldn't have any issues.
Some immigration offices might be willing to put a notation in your new passport that references your old passport number, but even with that it's not a guarantee for entry. The only sure way is to keep both passports.
Hmm. Maybe. I recall reading something about that but can't remember the specifics. I'm just used to telling people this since it's been this way for years.
The officers at the airport don't care about 90-day reports. Both when you are entering, and when you are exiting. It's only at an immigration office when you are there for something else that you can get dinged on this.
But if you already left and returned, then it would take an eagle eyed officer to notice that you failed to report the last time it was due. That means you should play dumb and never mention it. Just do what you need to do there, and if they don't notice it, you get to keep the 2000 baht you brought just incase.