Hi niksag and welcome to the forum
1 - you can play as many enhancements as you like assuming a lot of things (that you have initiative to play them, that they are the same brigade as your hero/s in battle, etc.)
2 - Yes, the character who has the banding ability must enter battle before the character they band to.
3 - If a hero is 6/7 vs. an evil character who is 7/7 then the initiative would belong to the hero because they would be losing (the ECs attack of 7 is killing their defense of 7, but the hero's attack of 6 is NOT killing the ECs defense of 7)
If a hero is 7/7 vs. an EC who is 6/7, then the initiative would belong to the EC because they would be losing for the same reason.
Just to add to your thinking...
If a hero and EC are both 7/7 so that both are dying in mutual destruction, the hero gets initiative because heroes naturally get initiative when it is a tossup like that.