I am sorry if this has already been answered, but I am on my cell phone and cannot seem to get the search function to cooperate.

HIGH POWER, LIMITED SCOPE: When using Mind Control, Kid Omega may target up to three opposing characters if all are within 3 squares of him. When using Telekinesis, Kid Omega may target and place up to three friendly characters if all are within 3 squares of him; when he does, he ignores those friendly characters for line of fire purposes.

Does Kid Omega's trait allow him to use Telekinesis to the full extent as long as those three friendly characters all start within three squares of him? Or, do all three characters have to both start and end with the final placement within three squares?

They just need to start within 3 squares. You can place them their standard distance.

All chosen friendly characters have to be within 3 squares if him when selecting them for his Trait, but after that you follow all normal rules for Telekinesis.

Sorry, but I am still unclear by what is meant when you say "selecting them for this trait". Can Kid Omega target 3 friendly characters that are within three squares of him, and place them 8 squares away, assuming LoF restrictions, and all other prerequisites for use of telekinesis are met?

Thats exactly what he meant. (When using this power/trait/situation)