Hi

I want to ask if such situation is possible.

Turn Start. Starbuck is in space area. She moves and then takes one action. She uses her second action to play Executive Orders on someone who is in Command. Command person uses two times Command location by taking 3 f.e. attacks with unmanned vipers and then launching another one... what uses Apollo by launching himself that way. And he has one action left. Turn ends.

Possible?

Yes that is a valid move - the chain of events doesn't break any rules.