How is overwatch triggered, and how is it affected by cover?

If a unit is in overwatch and an enemy moves a single step from a tile outside of the unit's vision to a tile inside the unit's vision, will overwatch trigger? How about the reverse - if an enemy moves a step from a tile inside the unit's vision to a tile outside the unit's vision?

If an enemy is on tile A and takes a step to tile B, and unit gets an overwatch reaction shot against it, does the game use the cover status in tile A or tile B? i.e. if an enemy is in full cover and I think it is likely to move next turn (Stun lancer, e.g.), would it be better to overwatch instead of take a shot, or will the shot consider the enemy to be in full cover anyway?

So, two part answer. First, Overwatch is triggered by moving more than 1 tile within the overwatcher's line of sight in a single move. You can move 1 tile without triggering overwatch, and you can move 1 tile twice (as part of two actions) without triggering overwatch. If you only spend 1 tile to move out of line of sight, you can continue your move unhindered.

As near as I can tell from looking at the SDK, overwatch shots will not benefit from cover, because they interrupt the move action, and the first part of the movement action removes current cover. (Though they don't count as flanked, either) There is also the standard overwatch hit % penalty of .7 (vs. moving enemies) and .6 (vs. dashing enemies).