So I asked to a friend from the USA what means formal (i think in italian it's just a bit different) and cool cat, because I know that cool is positive, but I didn't understand it well.

Ok, maybe you know this stuff already, but this is what she said to me:

"Yes, formal means he has very good manners.

As for cool cat. LOL, while the expression is an older one, it is very
complimentary. Back in the hippy days, cool cat meant you were the best.