For bsnes, accurate uses more resources to emulate more accurately. Some emulators aren't as accurate. They aren't exactly 1-to-1 compared to SNES. That doesn't mean they perform worse. In fact, it often means they perform better. But running better (or different in any way) means it's a less accurate emulation. The other versions of bsnes and snes9x are less accurate emulators, but require less resources.

From a practical standpoint, I'm not sure you'd even notice the difference between any of them. Snes9x takes significantly less resources than bsnes though. Unless accuracy is what you care about snes9x is the better option.

If I remember correctly, yes. But I can't tell you how well it runs. I use Snes9x usually on the Anbernic RG405M and occasionally bsnes-hd for wide-screen hacks on the Retroid Pocket 3 plus

The play store version is a bit outdated though. Use the APK from the retroarch homepage and choose your cores with the internal core downloader.

Nope, I haven't had any issues with save states. Keep in mind, there's a difference between saving the state manually and the option to auto save state when you leave the app. If you force quit Lemuroid or whatever goes wrong as you leave the app, the auto state save might not work. That's my best guess. I usually do both, save state myself, and rely on the auto save state. :)