That’s not correct. A single entry tourist visa gives you a 60 days stay within 90 days. A multiple entries tourist visa gives you several 60 days stay within 180 days. The validity of the visa itself always starts when it’s issued.
But your permitted STAY starts upon ENTRY, so in other words you get the permitted stay at any day within the validation of your visa, also the very last.
Formally it’s 90 consecutive days and until day number 90 have come to an end, you still haven’t stayed for 90 complete consecutive days so you can just leave.
If you want to do a report anyway you can do it online between 15 and 7 days before due time and manually 15 days before due time.
First 90 days report after re-entering Thailand you’ll need to do in person. After you can do it electronically. Ask your immigration regarding update of your TM.30 each time you re-enter. Some demand update, some don’t require it as long as it to the same address.
Yes you just show both passport in the immigration and you’ll get stamped in on the new one. You can visit your local immigration and get your stamps transferred to your new passport.