Highelf support card. "Action: when you play a development from your hand, look at the top card of your deck. You may put it on the top or bottom of your deck."

If I have multiple Barracks in play and play a development, does each one work on the same top card, thus being a waste, or do I look at the top card for one Barracks and then put that card at the bottom of my deck, then use the next Barracks action to look at the new top and so on?

When the first Barracks Action resolves and you put the card on the top of your deck, the next Barracks Action will hit that card too and give you the same choice again. If you put the card on the bottom of your deck, the next one will hit the new top card of your deck.

I just had a simmilar thought in my mind with a different card couple of days ago. If I have two copies of a card in my hand with action: give 1 power to each particular units in the battlefield and I have 4 that particular units in my battlefield then play both card in my capital phase; That means both cards give the same effects to the 4 units or just the 1st one? If yes it means I tripple up their power within one turn if all the 4 unit has got 1 power originaly? Is that correct?

Both effects apply, yes.