Yes, you do. usually, you are checked those 3 months when you apply for the next year's 1-year extension. They check it to see if you keep your current extension valid.
Haven't heard any other occasion much, but the possibility IO could ask to see is not zero.
TM30 is always valid with the latest submission. You need to do with your address when you are back, and TM30 dated later than any other TM30 records with your address is the one you need.
There is only ONE re-entry counter, and it is located on the passport control floor at International Departure Gate 2, before you go through the passport control/immigration officers. (hasn't changed for years)
IF you go through other international departure gates, you get through passport control, tell officer that you need a re-entry permit, then you will be directed to go to the re-entry counter at Gate 2 from the airside.
So as we always advise, go to Gate 2 is the easiest to get to the re-entry counter.