On both a 5500 and an SF, the opening wording to question 4 or 10 (and their a through i or n subsections) says, "During the plan year:"
So I don't think you're properly answering the question if you obtain it after the year-end but still suggest it was covered (unless retroactive).
And as for the "part of the year" scenario - I think it's reasonable to say that "the plan year" does not specify the entire plan year. Meaning, if you got your coverage on December 31, then the answer of "yes" is a true answer because during the year it was indeed covered. Heck, I'd suggest you get to leave "yes" as your answer if your policy expired on December 30.
(Recall on the SF, you're asked if the plan had loans, even if the they're all paid down to zero by 12/31, so you still admit there were loans, even if it wasn't all year long.)
As for the dollar amount, I'd use the largest amount of policy in effect during the year. Or if the plan just uses an inflation guard, I'd use the 10% BOY amount.