When you beat LP, are you able to go back and replay it with your leveled-up characters, like in Disgaea?

No, actually, so it really sucks. infact at the end you start losing characters ><

I just found out that there was a budget re-release of La Pucelle in Japan months after the original La Pucelle was released. You can start over in the re-release using an old save, and it has some other nifty features too.
So it depends on what version you have whether or not you can replay.

I notice to go to the next cycle of the game, is only in the PAL version or on the original japanese, I noticed that in the american game, they release some datas, like the real Baal, the second cycle and something with Baal and the title Overlord, that sucks I like complete games.