Phantom Girl from the Regular set.

After she makes a move action and uses her attack power can she target a nonadjacent character, that she moved through, with the close combat action?

Always quote the power you have a question on for expediency.

I underlined the key parts. She's done with the action, and the attack is made at that point, but she can target any character she phased through.

My question though is since she is using a close combat action wouldnt she need to be adjacent to the character she is attacking?

Normally. But her power allows her to target them anyways.

Otherwise, wouldn't she just have charge?

So how does range/line of fire effect this, I would assume that you could make that attack regardless. basically anywhere on the map. Thoughts?

It is a close combat attack that allows her to target a character not adjacent to her. It has nothing to do with range and line of fire, as those are not required for close combat attacks.