1) First with the unpardonable question: [...]
0.o

You've summoned the Kraken in me...
To give you a little insight, I'm a 'network-manager' hater (heretofore referred to as NM) from way back.
Accordingly, take anything I say, regarding NM, with a grain of salt. Most ppl would be wise to ignore my recommendation -- it's in the 'advanced user' realm. That said...
The first thing I do, on any Linux distro, is purge NM and install WiCD. Why? Because WiCD rules, and NM drools IMO.
Over the years, I can count a handful of times when NM (in various stages of development) actually worked for me, e.g. the things I do on computers --and NM did NOT spontaneously disconnect my machines from the outside world. This includes both wired and wireless connections, on a variety of machines, platforms, and OSs -- Peppermint included, on both desktop and mobile devices. Bottom line: NM sucks.
So, what is the answer, you may ask? WiCD
WiCD detractors will tell you it's an old front-end, no longer under development, and so forth, and so on. And, they're right, but... in my world view, that is a good thing -- because, once you get WiCD setup correctly, it_just_works. Period. Exclamation point! And, nobody is going sneak up behind you and change WiCD, while you're not looking. Personally, I hope they never update it.
Anyway, I'll stop my rant now. There is probably someone out there that likes NM and hates WiCD, and I don't want to get a flame war started.
If you feel adventuresome, PCNetSpec wrote a great toot over here:
http://peppermintos.net/viewtopic.php?f=11&t=5916It wisely deals with the overlooked vagaries that will confront you, when installing WiCD on a modern Ubu distro, such as Peppermint -- up to and including (dare I say) P5.
What I do is open Synaptic --> do a search for WiCD --> and install every WiCD package, except for 'wicd-kde'
Then, go to Mark's tutorial (linked above) and follow it step-by-step.