Is it possible to add my non-steam copy of FE to my steam account?

No, unfortunately not. They can't just give out FE steam keys to Stardock purchasers because there's no guarantee we'd use it for ourselves instead of giving it away. The only way to make such a transition would be to require everyone to use Steam, something they are unlikely to do on ethical grounds.

You can just add it to Steam as a "Non-Steam" game. That way you will still have the functionality of Steam and friends list. They will see you are ingame etc.

That's what I did, works fine. Besides, FE has no Steam achievements etc, and you will get the update faster than Steams release.

no.(not to have it same as other steam games).