1. If a LAT receives a Fall Back action during the Enemy Activity Segment and the LAT is at the top of the map, I assume you draw a new card to extend the map, as the LAT could eventually Rally and play a part in the game again? I've been playing that way and would draw a Random Result for the card, Top Left, Top, Top Right, etc, to extend that map (and as long as that card is out of LOS of US units).
Unless there's already a card there for the unit to move onto, it moves off the map and is removed from play.
This is found in the Errata and Clarifications for 9.2.2
2. I had an enemy capture two of my Litter Teams. Do these teams "disappear" (automatically transported) or are they stuck there until if/when I am able to take out the German unit, thus rescuing them?
Captured units go underneath the unit(s) that captured them, and move with the unit when the capturing unit moves. They also count against stacking limits when under cover, and have to check to see if they get hit when you're shooting into the card they're on.
So, yeah, you could potentially rescue your own units, assuming you don't accidentally kill them in the process.