Right now lets see here,

Question 1) If a person is based and Angel or someone with Carry is directly behind the intended person they want to carry who makes a break away if any?

Question 2) If the person with Carry ability is based along side a based passenger who makes the break away or do you make breakaway for each character both the carryied person and the person doing the carrying?

Question 3) If a team mate is based and Jean Grey wants to TK that person to safety is there a break away role required?

Question 4) now lets repeat the above questions with an enemy that has Plasisity shall we!

Question 5) is there any other situations i might have forgot?

Here is attempt to answer my own question according to my understanding of rules.

1)Angel would not make break away as Angel would be the one taking the action who is not based.

2)The person doing the Carrying would make a break away role but the passenger would not as again the person with carry is the one that is given the action.

3)Jean does not need to take break away to use TK

4) This doesnt change anything only the results needed to break away.

Do i have this correct so far.?

Right on the nail, all 4 are correct. Carrying is one of those awesome abilities that could make or break a game.

Thats why Lockjaw is fricken awesome in an inhumans team.