Jillian's orders were to find and croak the wounded dwagons. Ansom's initial plan would have been to retreat to the column to avoid being croaked by the dwagon ring (as Vinny says, it's a trap for Ansom). It's only after Jillian's proclamation of her love (via thinkagram) that Ansom acts out of emotion (not strategy) putting his life and Vinnie's on the line to save Jillian. If Stanley hadn't acted equally irrationally, the war might have ended already (Parson wanted to use the B dwagons to croak or capture Ansom on the next turn, but Stanley recalled them instead so he could go off on his own).
Thus Jillian was following strategically sound orders by not waiting for Ansom.
There is some debate about whether or not she saw them before she entered their hex, but my interpretation is that you cannot see units in other hexes.
Not to mention that turns end at the declaration of the side currently moving, and chronological events (such as nightfall) happen based on the turn ending.
Yes, however it is well established that units can only move on their own turn.
No, I didn't know that. I'm still pretty sure that Rob has stated that Erfworld was not written with a specific set of game mechanics in mind, and that they are determined as needed by the story. I don't have a link, though, so I'm not 100% sure.