What happens if I play Quagmire/Bear Trap on myself on AR 7?
Quagmire/Bear Trap don't go away at the end of the turn !
From the FAQ:

46
Q. Does a Beartrap or Quagmire end when the turn ends or will it continue into the next
turn?
A. The end of a turn will not end a Beartrap or Quagmire. Only the required die roll will
do so. Remember that neither card affects headline phase.

So, if you play it in AR7 you will not play AR1 of the next turn (except you played it in TURN10), you just discard a card and try your luck.