I am looking for a classic 500 for a restoration project. I was thinking of building a 595 or 695 replica. But I am also thinking if it would be possible to fit the classic 500 with the new twin air engine to create a new Fiat entirely. Has any one done such thing? Is it even possible?

I have seen some with Alfa v6 midmounted, Fiat Fire engine using the same gearbox. I think it is possible but with it mounted mid engined i.e cutting the fire wall.

Anything is possible really and I don't know if anyone who uses the rear seats in a Fiat 500.

Sounds like a great idea! I am driving a twin air presently and the performance it very impressive even in a fairly heavy body of the new 500.
A twin air in an old 500 would blow the doors off most Abarth 'replicas', my only concern would be what transmission you would use as the torque of the twin air could easily smash a 500/126 transaxle to pieces...