Untimed down or not?

[9redskin4]

I have two instances that happened in the same game.

Situation 1. A11 is running down the sideline as time expires in the second quarter. As A11 is tackled, B2 commits a facemask penalty. The clock had expired before the penalty occured. A accepts the five yard penalty. Does A get one untimed down before the half ends?

Situation 2. With time running down to end the game A is trying to get to the line a scrimmage and get a play off. With four seconds left on the clock, A commits a false start and the penalty causes the clock to stop with four seconds left. B accepts the penalty. Two questions here... does the clock start on the snap or on the ready for play? If the clock starts on the ready for play and A does not get a snap off before the clock expires, are they given an opportunity to run an untimed down?