My Skirmisher has ability "Back in Action". What will happen if he was killed and other hero use "Radiant Light"? For sure my hero will come back to game. Question is whether he can move additionaly just after that?

"Back in Action" (Apply +2 to your Health. Each time you stand up or are revived by another hero, you may immediately move up to your Speed)

"Radiant Light" (-->: Roll 1 red power die. Each hero in your line of sight (including yourself) recovers the amount of <heart> rolled. Each monster in your line of sight suffers the amount of <heart> rolled).

Its a good question and worth asking FFG. It depends on whether being revived is defined as removing your token from the map and replacing it with your hero figure following 1) a revive action or another hero ability restoring an arbitrary amount of hearts or 2) only a revive action excluding skills. Without further explanation from FFG I would choose option 1), as it allows for more use of Back in Action.

From my point of view I would say 2/

Indeed rulebook p15
"A knocked out hero may still recover damage from other heroes through
the use of skills, potions, and being revived (see “Revive a Hero” on page
10). If a knocked out hero recovers at least one damage, he immediately
replaces his hero token with his figure and may perform actions as normal
on his next turn."
revive is only one way of recovering damage, the other ways (like Radiant Light) are not "reviving".

but it's only they way I see it.. better ask FFG for the right answer ! :-)

There is no need to ask FFG. "Stand up" and "Revive" are specific actions described in the rulebook. They have similar effects, just one is the hero doing it to himself, and one is another hero. Other forms of recovering health are explicitly NOT revives or standups. You would be recovering health, but "back in action" would not trigger.

Good to know.