[Yvelina]

> - I have seen a number of troops with morale 50 "route" in battle

It probably wasn't a rout. An enemy flyer, or summon must have gotten in your rear, or maybe a trooper of yours got charmed/bound/enslaved... or even a summon of yours could have become a threat - horrors do, sometimes.

> - I have had at least 3 battles after which routed units end up in non-adjacent provinces

Theoretically, troops can take part in two battles per turn, and rout from both.