While I'm unsure about the exact innerworks of in-game breeding I can answer some of your other questions:
Rest is a garunteed 3 turn, self induced sleep. Early bird cuts durations in half. So instead of 3 turns of sleep, their would be 1.5. Obviously you cant be asleep for half a turn, and Pokemon hates decimals, so an Early bird rest would have 1 turn of sleep.
IE)
Turn 1 - Rest
Turn 2 - ZZZ
Turn 3 - Wake up
as for the simulator, it can be found and downloaded here:
http://www.pokemon-online.eu/ Pokemon online, PO, is strictly a competative simulator. All parts of the RPG are struck, leaving you with just the battles. You're given a team builder that allows you to customize everything from the mons in your team to their respective EV's and IV's. However, The simulator (or at least we do) limit "legal" move and ability combinations to those which are possible to get in game, hence it being a "simulator."
While I'm unsure of the exact list of bans for LC,
this link will take you to the list of legal mons. If its not on this list, it is not legal in LC.
Some of the mon's I do know are banned include:
Gligar
Misdrevious
Vulpix
meditite
scyther
Meditite
Though I know there are more, I just cannot think of them, or are incapable of spelling.
As for your issues with the RMT, make sure you're posting in the appropriate sub forum. And that you actually hit "post". Sometimes i hit preview and then go away.