My question is does each fig with the Avengers TA get to choose a different target, or does the team as a collective choose a target?

I'm pretty sure the team a whole picks a target, instead of each member, or they would have used the word Each instead of all. Otherwise, if each member could pick a different target, the phrase "An alpha flight team member..." would allow each team member to increase their attack value against their own target, and each others target.

Just asking because this Alpha Flight ATA, is written differently than the Ultimate X-men TA. I haven't Used Alpha Flight ATA on multiple figs yet, and I was just comparing the writing to Ult. X-men and 2000AD.

It is one character or team for the whole team. It works really well during theme team play. The addition of keywords for theme team made this card devistating on avengers, alpha flight, and Thunderbolts.

Only a specific Character or Team Symbol can be chosen, correct? A team keyword can't be used as the team chosen can it?

Correct. It's a poorly worded feat, but it was from Seth's first batch...

It works like 200AD, not like Ultimate X-Men.