We've mostly gone in Oct (and are hoping to again this year). Leverick has always been open, although I think the upstairs is closed. I'm pretty sure Coopers was open before Oct 20th 2019. I don't recall the actual date we were there, but I thought it was before the middle of the month.
Foxy's was "open" but I think we were the only four tourist on the island.

Marina Cay was closed in Oct even before Irma. Scrub Island is open. Soopers pre-Irma was mostly open; Post Irma it was not rebuilt when we were there.

I think Peter Island is closed.