When pressed, only the selected inputs are heard. There should be a special knob to set the level of solo monitoring so you don't mess up any settings trying to check a quiet source. VU meters may be connected to various parts of the mixer. Shutting off the control room speakers prevents feedback through the recording mics. This is very useful when the tape is played later.
TONE provides a sine tone of calibrated amplitude on the main busses.
The tone is usually available at the patch bay as well. As with any musical instrument, virtuoso ability with a mixer is only acquired through long practice. To get this practice, you should use the mixer for monitoring any time you are in the studio, and you should make several mixdowns of all of your multitrack work. There are many ways to set up a console for mixdown, and they will all produce pretty much the same electrical results. As you try various approaches, you will find some easier to use than others.