The manifold as far as I know is not a straight swap, the abarth engine is incredibly tightly packed in the engine bay of the 500, even the badge acts like an air vent on the abarth to let cooling air in as it’s all so tight. Because of this the abarth engine does not sit exactly as the 1.2 engine will it uses a different gearbox, different drive shafts and different front suspension set up, most likely with different splines on the axles. You could make customs drive shafts but you would need them balancing afterwards and to know an exceptional welder.
The turbo on the 1.4 is matched to the multiair set up, I believe it’s a variable vein turbo, something your 1.2 ecu will have no provision to control. Neither will it have the ability to monitor boost pressure.
In the 80s when cars ran carbs and nothing electrical you could in theory bolt on a turbo, tweet the carb and get more power but it did require some know how, but could be done at home.
Knowing people who have build and installed customs turbo installs as well as following a few threads on this forum your choices are,
1. custom made parts, customs fitted and a bespoke ecu. Which can cause problems with how the rest of the car works.
2. You buy an abarth engine with all ancillaries and gear box and try to install it, still have to replace bodywork because the body was made to fit that engine to the abarth (so you’d not have a sleeper) then try and get it all to work and talk to each other without access to the Fiat Examiner system needed to program the whole lot to work properly.
3. You buy a £4K abarth as is and enjoy it. Which would still work out cheaper and more reliable than options 1 and 2.
4. Buy a motor bike which will go faster than most cars anyway. (Cheapest option, but most likely to get you dead)