This was assuming it gets tested and isn't asbestos.

It doesn't look load bearing but it's hard to tell without seeing the full framing of the joists. If you're worried it is you can still add your shelves, just frame it with a 2x6 header to transfer the weight to the side studs like you would a door opening.

If you get the heavy chunks of mastic on some floor refinished might be willing to just use a belt sander with a really aggressive grit for the remaining bits. It gunks up the drum and wheels on the sander so many will refuse to do that. I've done it a few times and it worked well, just needed to clean the machinery throughly afterwards.

Hardwood floor guy here. If you do this with the steamer and it works let the floor moisture content lower back before refinishing it. I'd recommend about 2 weeks to let it dry and reacclimate to the house's humidity.