When Thanos on issue #1 and his exile to the soul world activates does the character keep action markers and its object?

You should quote the power...

Updated...!!

They would retain any tokens they would have had, unless they would have cleared by the time they were brought back.

it would keep action tokens and any assigned relics or resources. I believe a held object would be dropped in the square they were in when removed.

Thank you very much.

What if a character can't be given a double power action "at the beginning of the next turn"... are they forever stuck off the map, never to be returned?

The ruling for similar wording in the past is that there is always an "at the beginning of the next turn".

It doesn't have to happen at the beginning of the next turn that they're exiled, but if the beginning of the turn has passed, they have to wait until the beginning of the next turn before they can bring them back.

This is wrong, see below.

Gotcha! I remember there being a similar situation with the flashpoint flash but couldn't remember how it had been ruled. Thanx!

If there are no opposing characters in the map, immediately return all characters removed this way to the square(s) of their owner's choice.

Looks like I'm wrong on the 'next turn' thing. Next turn is the turn after they're exiled. If you can't rescue them on that turn, then they're stuck there until there are no characters on the map.

Flashpoint Flash was changed to remove the 'next turn' and just say 'at the beginning of your turn'.

Wow, so in most cases you will be damaging Thanos by attacking him, thus giving at least one action token, making it impossible to ever give a double power action on the next turn. You attack and you run the risk of losing valuable figs to wait until they are all "in the soul world" or ko'd... wonder if Thanos will receive similar errata like Flash.

The power says:

An opposing character may be given a double power action to return the removed character to the map in a square of its owner's choice at the beginning of the next turn, even if this power is lost.

The "next turn" is in reference to when the power action is given. It does not reference the next turn after the character has been exiled into the Soul World. If it would be, then it would be written like:

At the beginning of the next turn an opposing character may be given a double power action to return the removed character to the map in a square of its owner's choice, even if this power is lost.

Just when I thought I had the power all figured out....

So does the character need to be given the double power action right when the attacker gets exiled and only then? Or can they be given a double power action at any point during any of their turns to get their guy back at the beginning of that next turn?

You don't give the banished figure the DPA, you give it to a different character to bring the banished one back.