See if I can answer some of your questions.
1. The general rule is one horse per race, although there are a couple of exceptions like the Grand National
2. The season lasts 13 weeks, so in theory a horse can run every week provided there is a suitable race. Normally I find there are only about 10 - 12 races a season for most horses as they have to abide by some distance restrictions, flat - 2f and NH - 3f either side of their best run.
3. Yes there is a website called TOM where you enter horses into races. It is here
http://startersordersonlineleague.com 4. See the League Rules thread at the top of the forum.