You can go back but by the time you can, the experience from the early leagues isn't worth doing. Nor will the fights be challenging at all.
That's not correct. The enemies will ALWAYS scale to your party's current level. So a fight from the very first town you encountered will have high-level enemies if you revisit it at the end of the game with party members at level 20.
You can only advance to the next region after you've won all the necessary badges and tournaments for that region, and then won the championship match for that region. Then you are allowed to advance, but you don't have to go right away if you still have other quests to do.
I highly recommend picking up the official Strategy Guide for this game, if for thing else than the excellent summary of all the available gladiator classes in the game. I was constantly referencing it for various skills and abilities.
Great game, I put in 106 hours to beat it over a 4 month period.