This could have been a coincidence but I feel like it was too exact to be one. The second I blocked the exact tile they wanted (with my military unit we weren't at war) they stopped their settler and moved him back to their capital. I had a unit nearby and the AI started moving their settler there. With 3) the only time I've noticed this was when there was one good opening in the entire area for a city. 3) Wait for a position to open up then move it.2) Wait for a military unit to escort it.
When playing I've noticed that an AI opponent will do one of three things with a settler: I'm not sure if this is Comment or Answer worthy as it's mostly speculation at my own experiences but here it goes (The way I see it is this might not answer directly or completely but it may help give-way to other answers and/or possibilities):
