Facebook is able to track you quite successfully almost everywhere unless you block them using an anti-Facebook blocklist with a decent ad-blocker such as ublock origin. At the very least, everywhere you see a “share on Facebook” or a “like” button, you’re being tracked by Facebook
Mozilla, sadly, isn’t really that trustworthy anymore. A VPN is not really helpful when it comes to ensuring privacy - a VPN hides your IP address from sites you connect to, but cookies, browser fingerprint, login accounts, etc. are much more useful than your IP address because your IP address is likely shared with other users, potentially many others. And additionally, you’re trusting the VPN provider with far, far more than you really should. It would be pretty straight forward for some VPN provider to steal your login details for basically any website if they wanted to do so.
For emails, disposable email address providers exist and if you use Bitwarden password manager (highly recommended!) then you can use them to generate username/password combinations for any website you like.