1) If the enemy activity draw orders the unit to "seek cover" and there is already cover on the card, does it move to that cover automatically? If not, and the card is at its max cover limit, I assume it's "no action" as per the instructions for actions that cannot be followed?
Yes, he takes cover if it is already there
2) When a pinned unit is no longer under fire (i.e. the firing enemy unit pulls back), at what point do I remove the pinned markers? Since this could well affect the type of VOF in combat, it might swing things on a turn or two, and I can't remember where I found that in the rules.
At the end of the Combat Phase