Audacity can do everything in that list short of Punch-In. Amplify, Normalize, Compressor, the lot – but in post production. Audacity does not apply effects and filters in real time. You really do have to get the recording right without a lot of digital help.
It may be harder than you think. We’re on chapter three of a poster who wants to do a simple interview recording.
https://forum.audacityteam.org/t/newbie-needs-both-immediate-and-longer-term-help/29486/1
The longest posting on the forum, ever, was someone who wanted to simply record his acoustic guitar.
Koz