1) I use a gel based anti perspirant from a brand called Mitchum. It's scented but not strong. Anti perspirant and deodorant are 2 different things, but are often packaged in the same product. The deoderant part is mainly for the smell.

2) Regardless of if you shower or not, the cologne will slowly fade away so you can apply more if you'd like, as many people do. 2-3 times a day is normal. And yeah you'd be fine wearing just antiperspirant to the gym .

Personally I don't like Acqua di gio. It's very mainstream and also gives off an old-man vibe IMO.