1. If I have a few weak units, can I attack some objective and get bonus unoppossed damage each time? Looks overpowered, as I can have 5 units and my opponent may have only couple blockers.
2. If he has no blocker, can I attack with unit without damage signs and get bonus unopposed damage? think R2D2.
3. If I have exhausted unit, can I play action listed on him? And what if it is not action but reaction? Do i need to exhaust a unit when I do that?
4. Can I attack same objective few times?
1(&4)- You can only attack each objective once per active turn. So, yes each successful unopposed attack gets the bonus.
3- Yes, as long as the action does not say the unit has to be focused to use it.