Manage /etc/hosts from menu bar

This is likely a status item, not a menu extra. (Not being able to move it around or remove it by holding ⌘ and dragging is the way to find out.)

In Activity Monitor (in /Applications/Utilities), set the pop-up menu to "My Processes" and look for anything that sounds related to the scanner vendor. Also, check ~/Library/LaunchAgents for a file that mentions the vendor in its name. Lastly, check System Preferences → Accounts → (your account) → Login Items.

I've been annoyed by this, too, and the simple, yet very, very painful answer is to hold alt ⌥
option and press the green title bar button (which should turn into a + when you hold option/alt)

If this doesn't make it cover the screen, you can finish the job by holding alt ⌥
option and double-clicking a corner to resize the window to fill the screen.

If you make your dock hide by default, this essentially gives you a "fullscreen" program with the menu bar always shown.