Hello, i have a question, if a character or Specialization Deck from Age of Empire, can be used in Force and Destiny (or Edge of Empire)

and Vice Versa

The specializations are completely compatible across all 3 systems. The Three core rulebooks are essentially different facets to the same game.

There are a few cases, such as many of the talents in Force and Destiny would be useless to character who is not Force sensitive, and there are a couple of talents in Age of Rebellion that play with the duty mechanic, but those are the exception, and in the case of the Force talents, can be fixed by using one of the Force Sensitive universal specializations.

To add to what @kaosoe said regarding those AoR Duty related talents. It is perfectly reasonable, and expected that if you’re combining all three lines that all three mechanics (Duty, Morality, Obligation) can be in play at the same time as well.

The F&D core book has several pointers on how to use all three in the same campaign.

It's also worth noting that some specializations are present in more than one line. The pilot specialization is in Ace (AoR), and in Smuggler (EotE), Mechanic appears in all three. You don't get to retake a tree just because it appears in multiple careers.