"What I am wondering is what backs are available for it."
Spring back (Graphic back) or Graflok back. Maybe Graflex back as well, if I am remembering my terminology correctly...At any rate, the one you hope to get is the Graflok, as it takes the roll fim holders.
"I saw a post that said 22 and 23 backs are available. Will any 23 back fit or does it specifically call for a 23 back made for a 2 x 3 camera? I would like a back that holds several sheets of film at once and one to use 120 film with."
Yes, 22 and 23 rollfilm holders, and they have to be made for 2x3 format. There are also 4x5 and 3x4 ones, so watch out and get your measurements from sellers before buying.
For several sheets of film at once, you can use a Grafmatic holder. Yet again, these are not the most common in 2x3 size. Make sure you get measurements first.
Also, the later RH-designated lever-advance rollfim holders are reputed to hold the film more flat than the earlier knob-advance backs (22 and 23).
"I've asked a couple of sellers on a famous auction site and none of them knew for sure which back I needed."
I have no idea how these EBay fools even get a hold of this stuff, and given that they know nothing about it, how they even manage to sell it at all. Buyer beware. Know your stuff before bidding.
"Is there a source for color sheet film or will I need to cut my own from larger film or should I use the 120 and be happy with it?"
You will have to cut down your own from 4x5 sheets in absolute darkness. When I did it (once), I made a wooden template from a piece of factory-cut black and white film. It is not hard after a few tries, but you should only bother doing this if you will be doing individualized processing for each shot. For instance, if you want to push one shot one stop, pull another one stop, process one normal, etc. Otherwise, you are better off with the rollfilm backs. Even with rollfilm, you can carry three (or more) backs, each marked with a different development. It's worth the investment in multiple backs, IMO.
"And finally what is the thickness of the factory lens boards? My camera didn't come with one."
Pretty thin. They are sheet metal. The most important part is building the light trap properly. You can make them too thick and tape them on if you need to, but the light trap needs to align with the ridge on the front standard to keep light out. I would just buy one, as they are very cheap. Check out KEH.com for holders, rollfilm backs, and lensboards.
If you decide you want a sweet 180mm Schneider Tele-Xenar lens for it some day, let me know. I might consider selling mine. I am loath to do so, but the truth is that I just don't use it much any more. Great headshot or landscape lens, and teles can come in handy on a Graflex.