The objective reads:

While this objective is undamaged, it gains: "Interrupt: When you would place a card into an edge stack, you may instead look at the top card of your deck and place it facedown in your edgestack. (Limit once per edge battle.)"

If I have two copies of this objective on the table can I use the effect twice per edge battle?

Yes. The template "Limit once per x" applies seperately to each copy of the card in play. For similar reasons, you could use the Repair Droid's action twice if you happened to have 2 in play or use Darth Vader's reaction twice in a turn if you managed to have 2 copies of Darth Vader in play that turn (obviously at different times, I've actually done it once).

This is different than the "Limit 1 per turn" template found on cards like Force Choke or Rebel Assault. In that case, only one copy of the card can be played per turn.

This is how I remember those cards played. But where can I actually find the rules for the difference of a limit on an events and other cards. If the other player has a doubt I have to proove it.

These have been previously confirmed with the development team, and they should be in the next version of the FAQ.

Ah thank you. In Game of Thrones it is played this way as well but that is not so convincing to other players. And of course they do have different designer tastes. You may search and not find in Star Wars even if there are legal targets (you know the bulk transporter) while you are not allowed to do this in Thones or Cthulhu. Speaking of development team... Do we know other designers for Star Wars than Lang and Nate?

Another question regarding this card: If I choose to use the objective's ability, am I obligated to add the top card of my deck as my edge card or can I peek and decide to just leave it on top of the deck? If I can "peek first", then would I be allowed to play a different edge card from my hand? If you are forced to play the card from the deck, then what is the point of the card text saying to look at the top card of the deck first?

The interrupt is optional, but if you choose to execute the interrupt, then you must complete it. The second part says "and place it facedown ...", so you must do this. Otherwise it'd say something like "and you may choose to place it facedown ...".

The effect says to "look" at it simply to make it clear that you're allowed to know what you've just put facedown in your edge stack, otherwise it would move from facedown in your deck to facedown in your edge stack and you'd be in the dark.

Strictly speaking, the look at it part of the ability is currently redundant as you can look at the cards in your edge stack already. However, if there's ever an interrupt ability that interrupts placing a card in the edge stack you might appreciate knowing what the card was as the effect would go off before the card made it to the edge stack where you could look at it.

True. When I was typing, I was thinking that if it didn't say "look at it", we'd be fielding the question of whether you're allowed to look at it. Sometimes an effect just can't win.

Another question :
If I will use this objective and opponent play a card Twiste of Fate, can I use this objective for the second time ?

Twist of Fate final sentence : "start a new edge battle"

Last Defense final sentence : "(Limit once per edge battle.)"

Answer : Yes