A cat back exhaust won’t do anything for power but they sound nice.
Tuning is just a generic term for ecu calibration via several different methods. Cobb is the most popular but I believe there is some open source tuning solutions as well as ecutek.
On the fa20f the biggest gains are to be had in the intake. Some of the common first modifications are an intake, cat back and supporting tune.
Things can get hairy when you don’t know what you are doing. The easy path are Cobb staged packages that sell you the parts and access port to load the correct tune to the ecu. You can get better results by speaking to your local tuning shop and buying the parts they recommend and having them do a dyno tune.
With tunes parts are not interchangeable on the intake. That means a grimmspeed intake will not be supported by a Cobb off the shelf tune and will require you to have a custom tune done. Or if you have a cobb intake and the off the shelf tune you can’t use it on a Perrin intake. You’ll have to have a new one made.
Now exhausts are a little more forgiving. A 3” catted downpipe regardless of brand will be supported by just about every tune for one so you can grab a turbo back exhaust setup and use the appropriate Cobb tune provided by them.
So any mod outside of a cat back requires some form of tuning solution. Intakes downpipes, tgv deletes, egr deletes, headers, wastegates, turbos, injectors (although you likely won’t need any with the direct injection).