If you take a look in the Orbiter manual (docs folder) you will find a full list of controls. Yes its entirely possible to use orbiter with just a mouse and keyboard. Atmospheric flight benefits somewhat from the use of a joystick, but it's possible without it.
I don’t have a joystick, strictly keyboard and mouse here. Atmospheric flight is a bit annoying. Space flight and ascent/descent works well. You’ll need to learn to use the aap and/or gimballing for atmospheric flight, or various add-ons available.