Sorry if this has been asked and answered. Can the Falcon after being focused to attack and after the resolution of the attack, can use his action to bounce it to my hand to play a character. In other words, can a focused card still use its printed action.

Thanks

Yes, the Falcon can bounce back to your hand even whilst focussed.

Yes, you can therefore attack objective A with the Falcon, focus it to strike, and resolve the combat. Then bounce it back to your hand to put, let's say, Han into play.

Han can then attack objective B during the same turn

Thanks, that's how we played it. Just could not see a reference in the rule book.

Exhausted (focused) cards can still use their game text, as long as it doesn't say something like "focus this unit to...", in which case it does have to be ready (unfocused) to carry out the action.