To answer your first question, Netflix doesn't know your password.
What Netflix and every other competent website out there does is hash your password using a one-way hashing scheme (MD5, SHA-1, SHA-2, etc.).
What this does is essentially create a unique fixed-length hexadecimal fingerprint that identifies the string of text that is your password. For instance, here's what my-secure-password looks like after being hashed using MD5:
They store this hash in their internal database and every time you log into Netflix, the password you supply during the login process is hashed once again using the same scheme and is matched against the copy of the hashed password stored in their database.
If they match, they know that you've entered the correct password and you're granted access. If they don't, you're not authenticated. This is why when you click on some variation of the Forgot password link they don't send you your old password but rather ask you to choose a new one. It's because they don't know what your password is either.
So how are you logged in if Firefox did not store the password for Netflix?
The answer to that is session cookies. When you logged into Netflix (maybe a while ago), you may have chosen to remember your session.
If you did, Firefox stores a small tidbit of information on your computer that uniquely identifies you whenever you visit Netflix. These 'cookies' as they are called generally persist for a short period time until the session is active and then expire. Some however may last weeks or longer. Delete that cookie and Netflix won't remember you.
Regarding your second question, if Firefox didn't 'remember' the password, it isn't stored anywhere. What's stored is the cookie. Firefox stores them in its Profiles folder in the file
cookies.sqlite which is a SQLite database file.
Lastly, if you opted to log in through your Facebook account, you wouldn't need a password and so Firefox wouldn't store one.
However, a cookie would still be created to identify your session.