To 1 and 2)
Cryptomator desktop needs the vault files local available. If your storage provider does not support „files on demand“, then you can try cyberduck instead of cryptomator. Cyberduck does connect directly to your online vault. See here: How do I use Cryptomator without local sync?
To 3)
Yes you can. You select the vault path when setting up a vault or adding an existing one. The file path is shown in the app on the left side right below the vault name.
To 4)
If your vault is stored online, and your physical drive dies, then you can recover the vault from your online storage (same as it is with any other files). If you do not have your vault online and do not have any backups, wenn then your vault and the files in it are gone. (Again; like with any other file too)
To 5)
The content of your masterkey file is not your key and it’s useless for anybody without the password. But it’s needed to open your vault (together with your password). That’s why it is stored next to your encrypted vault files. See here: Why is the masterkey stored in the cloud?