1. after looking at it, i've changed my mind. i'll post what i saw in OR below but to summarize: we have 50% equity against a range that consists of only 3% of his pre-flop range if you give him all hands minus the top 10% of hands (i used this 90% bottom of hands just to demonstrate that if we give him stronger hands it's still not that bad for us) and calling can lead us to some tricky spots OOP on turns. i've overestimated how bad it is for us to run into a TP/MP+NFD type of hand, and this is only 25% of the 3% nutty part of his range that gets to the flop (so less than 1% of the time he gets to the flop).
so even if he raises this tight of a range, it's fine to get in. and we're still 42% or so against these TP>+better FD type of hands that would want to raise the flop.
2. if we did call flop, i would assume checking when we hit most of the time since it's rarely going to be the nuts and our calling range is going to be sort of weak in this spot (given that we didn't 3bet the flop and especially given that we didn't raise pre-flop ourselves, that takes out a lot of strong hands from us too)
100bb i would say definitely call because even if we 3bet the SPR is going to be higher on the turn and we'd be more prone to making mistakes since villain is going to play well + have better hands than us on a lot of different turn cards (better flushes on hearts, still have good made hands on blanks, etc.) and we'd just be punished more for putting in that amount of bb with a worse draw/made hand