1 - If a team consists of five Avengers - Jolt, Hawkeye, Songbird, Shaman, Wasp - Two of them - Jolt and Songbird - are slammed with Thunderbolts cards - so their TA will be Mystics - the Assembled BFC is still good, if Jolt is adj. to Wasp, making an +1 attack?

2 - if Assembled and Disbanded are put down, which one negates other? Disbanded?

Thanks.

if you use thunderbolts every avenger has to use it, you can't choose between who will be thunderbolted

okay hmmm....maybe setting that one as a bad example....hmmm....as you can see, I am involved in a league using house rule - we made an agreement that only Jolt, Hawkeye, Songbird, Meteorite, whoever is a member or a former member of T'bolts only gets to use the T'Bolts card instead of the whole Avengers team. so I will have to think something else to make a good example...oh well.

What about my second question?

Disbanded would negate Assembled, as it says "Ignore all team abilities", and Assembled is predicated on the use of a TA.

This is incorrect. Disbanded! does say it ignores all team abilites, true, but Assembled uses team symbols, not abilites. Even with Disbanded! in play, all Avengers still have the Avengers team symbol on their base, so they would still (potentially) benefit from Assembled. This is the same reason Sentinels (or Sinestro) are still AEs with X-men, Brotherhood, Morlock, etc (or Green Lanterns) when Disbanded! is in play.