I'm not sure. What engine is the 1600 16V? If it's based on the old Tipo engine, then yes, it will fit with an ohc non FIRE Uno gearbox. But other than that I've no idea Where is the 1600 engine from? A Lancia?
Sorry, I don't have a clue
I don't think many countries have the Palio.
Chas, I found a page about the Palio at http://www.carsfromitaly.net/fiat/index.html, and it does look like you may be right; the 1580cc engine (with bore 86.4mm) sounds a lot like the venerable Tipo 1.6/old 128-style motor!
Sounds like a fun project! Can you get the engine fairly cheap?