I had a question about Lt. Gordon from DKR set. He was played at my venue recently and we were not sure how to rule this.

GET THESE MEN INTO POSITION!: Give Lt. Gordon a power action; you can immediately give him and up to two adjacent friendly characters who possess a team ability or keyword possessed by Lt. Gordon a move action as a free action, replacing all characters' speed values with Lt. Gordon's unmodified speed value.

If he is adjacent to a character that can carry, can that character carry Gordon as its free move action, and then Gordon take his move action?

If both a vehicle and another character start adjacent to Gordon, could the vehicle carry both Gordon and the second character as its free move action, and then both Gordon and the second character get their free move action?

The power says immediately, but I was not sure how that would interact with figures being carried. I think when it comes down to it, they all get a move action as a free action and you can't do them at the same time.

You can do that provided your move actions are all free actions.

You have to resolve 1 action at a time. The immediately means you can't activate Jim and then do a few attacks and then free move a Batman later.

They couldn't do anything else other than other free actions since they were carried.

Soapbox - I despise Free Actions that allow moving and attacking due to the obvious ease of abuse. Gordon's ability is neat if it was balanced with "lower point value" since it would really be him moving his guys into position instead of being a way to abuse a cheap mechanic (Cruiser's Clear the Streets). Not that you were planning on doing it - just Free Actions as moves / attacks are worse for the game than Spiral, in my opinion.

Follow up question. If a figure adjacent to Gordon has applicable modifiers to their speed, those would kick in on the free move action, correct? You are replacing their speed with Gordon's, however you would then modify normally?

Yes. The speed value isn't locked so any modifiers would apply.

Replace and then modify.

Replace with Gordon's in modified defense. Then add any modifiers.