That's 4 factor :)
Pain to remember, but it's definitely secure.
That's one-factor authentication.
Two-factor means you need two things, not just the passwords, but for instance also a device.
You mentioned a remote key, so yes, it sounds like you have two-factor. But not four.
Fair point about the keylogger. I didn't consider that - it's not my network to worry about :)
That's 4 factor :)