Untimed down
 

Near the end of the first quarter (Or any quarter), the clock is running. With 10 seconds on the clock, A (a) false starts, or (b) has 2 men in motion at the snap. In either case, the penalty is accepted, the clock is wound on the RFP, and time expires in the quarter. My interpretation of the rule is that you would have an untimed down in (b), but not in (a) since the false start, being a dead-ball foul, didn't actually occur "during the last timed down". Am I correct??

you are correct.

This is another NF-NCAA rules difference since the wording in the NCAA rule is "penalty is accepted ..... that occurs during a down in which time expired". So in this example neither a nor b would result in extending the period in an game played under NCAA rules.