1. Do Carbuncle use TP? Like my PUP i have TP info macro in all my summoner macros.
All avatars have the same behavior regarding TP: It is used to boost magical moves only, and does not affect physical moves. For example if you use Poison Nails, it will not consume Carbuncle's TP. However, if you use Healing Ruby or Meteorite, they will both consume the TP and their accuracy/potency will be affected by it.
2. What are the elementals used for? I bought them all from AH and light buff and quick fire summon backup is all I use.
They are used for basically nothing, except Elemental Siphon. Folks have struggled to find uses for these, but they are generally pretty lame.
3. What skill should a summoner be to start the level capped avatar fights? My skill is close to 80 and i think i read somewhere 68 is the Lev 20 cap....Any help will be appreciated.
I believe the cap at 20 will be about 93 skill. You should absolutely cap it before doing those fights, as it's very possible, even likely I'd say, that you will be hit once or twice while attempting to resummon Carbuncle. Summoning skill helps your interruption rate immensely. Sadly, that's about all it's good for until you reach the upper levels and start getting equipment that can push you well over the cap for skill.