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Yes, it does. I do this for multiple folder- i.e. the pictures folder on my phone is called whatever android has decided to call it this year and it syncs with my pictures folder on my desktop.

I'm not sure it's supported in a GUI, but a simple symlink should do the trick. Say your photos folder is called Pictures on one machine, and Photos one another: just ln -s Pictures Photos (admitting you've moved all the contents of photos to Pictures and removed the Photos folder itself) and that should just work (didn't test).

You don't need to do this: when the folder is offered to share to another device, you can specify which folder it's going to go into locally. Internally everything is matched by folder ID codes.

Yes, it doesn't care where each folder is on the FS or what it's called.

be careful with upper and lower cases. some file system doesn't distinguish them.