Not necessarily. You might be able to get away with a very light window manager, but some of the more memory hungry ones like KDE/Gnome aren't likely going to be available. In that case you wouldn't be able to boot up into a gui login screen, but you could boot up into X after configuring your box to start your smaller window manager.
As for logging in:
It's the standard. I don't really know what to tell you other than you fed a password (or requested not to have one at all) to your install about root (you apparently don't remember this
). It is the system admin of linux and is password protected for your protection. If you cannot remember the password, then search this site for "single" or "linux single" to find out how to boot into single user mode and recreate a password.