Was looking at Kyle Rayner and wondering how this works with the newer wording. Can I assume that it becomes standard Telekinesis?

Option 2 would be the non-combat version of TK.

Follow up question about TK on this part:

Give this character a power action and designate a target
character or object (A) and a destination square (B). This character, A, and B
must all be within 8 squares and line of fire of each other. Place A in B.

Does the character using TK need to have line of fire with destination square (B), or is it just between A and B?

the character, A and B all need to be within 8 squares and LOF. So the character needs to have LOF to A and B and be within 8 of each. A needs to have LOF to B as well, and be no more than 8 away. And there needs to be LOF from C to both A and the character.

All three need to have line of fire with each other.

Awe crap! I think this is where I missed it...

This character, A, and B must all be within 8 squares and line of fire of each other.

My bad guys

The rules text you posted answers your question.

"This character, A, and B must all be within 8 squares and line of fire of each other."

The best way to remember it (to me at least) is that it's a line of fire triangle, with each point seeing every other point.
One exception would be pulling something straight towards you.