Welcome to PRO! :3
I'm a 2 weeks old player, so I still consider myself new. But I think I can help you with those questions.
1) Your pokemons will be locked up just until you get the Johto's 8th badge. Then you can use them again.
2) After you beat the 8th Gym, you can go back to Kanto.
3) I believe that for now you can only find eevee in kanto's safari. You can get Larvitars in Mt. Silver (after you beat Johto's e4)
4) No, people wouldn't buy mounts that way :P And it's a money sink on subways. There may be another reason but I think Fly outside the battle is never going to be implemented.
5) TM80: Shadow Ball - Deathwing Boss Battle Reward / Celadon Daily Quest Reward / FOUND in Hall of Fame / Lilycove Department Store 3F $4,000.
For future reference check: https://pokemonrevolution.net/forum/viewtopic.php?f=120&t=29668
6) When you try to teach a TM/HM on your pokemon, you'll get a message in the chat (green text) that it learned or it can't learn. But if you want to check beforehand, you can check on pokemondb.net or similars, that tell you what it will learn by leveling up, and which HM and TM it can learn, as with Egg Moves (I don't know anything about these yet).
EDIT: I was too slow T_T