If I was in your position, I would lightly sand the burrs until they were gone. As far as the separation goes, I’d leave it alone and check it every few months. Heck, if it opens up more, it’ll be easier to repair.
A ply separation would have made me sick several years ago, but after messing around with vintage drums for a few years now, I don’t see it as any big deal. I’ve glued and clamped re-rings on every vintage kit I’ve bought. Usually, something needs work.
Wood is a funny thing. It’s takes a while for wood to stop being a tree and start being an instrument. In the meantime, it can do weird stuff, and that’s ok. It can be unpredictable and do weird stuff as it dries and settles.
In terms of tuning, there is a ton of great info out there. My thing is if I have a snare that I can’t get to sound good with good quality heads (usually single-ply coated or a coated reverse dot + a good snare side), cheap snare wires, and a snareweight m80, I get rid of it. I don’t have time to fiddle around with a finicky snare drum.