c1 and c2 are probably referring to categories (edit: this is wrong, see cardstock's response below). cat 1 is the fastest, down to cat 4 (which is where you'd be starting). uci and usac are separate organizations with slightly different rules, but i was able to use my usac license at the uci event i did last season (i'm not sure, but it might be that technically only the "elite" race was uci, it's worth checking with the race organizer).
uci:
http://www.uci.ch/templates/UCI/UCI1...MenuId=MTUxMzY
usac:
http://www.usacycling.org/
this site will list most of the upcoming races:
http://www.mabra.org/
here's where you'll go to register for races:
http://www.bikereg.com/
regarding small cross bikes, the motobecane fantom cross has a "size 49" although i don't see an effective top tube length on the site. it's probably also worth taking a look at some mountain bikes. if you find one that's not too heavy you could put some drops and bar end shifters on there. maybe some slimmer tires, and she's good to go.