What I find most interesting is the rule allows the clock to run through that 5 minutes left mark in the 2nd half. Last night the Chiefs had a player go OOB at ~5:05 left in the 4th. The officials spotted the ball and the clock ran down until ~4:45, when the Chiefs snapped the ball.
I dont believe that your second statement is true. If the yardage is given for forward progression, then the clock wouldn't stop. If they run out of bounds backwards, then that is the players intention, and the ball is spotted where he goes OOB. If he catches a ball and is tackled backwards OOB, the clock would not stop because the player did not intend (make a football move) to do so.
Bolded statement is also untrue, there is no reason in that situation for the clock to restart. The player intended to go backwards OOB, clock is stopped until next snap.