1) I use Mantis (www.mantisbt.org), because it is simple and works.
Don't know if it's got an API for generating tickets based on email, but
I guess that could be a part you invent...

I looked into Bugzilla, but it looked way over-complicated for my needs.

2) Probably my favourite forum is Vanilla (http://getvanilla.com/). It's
very good looking, but it's slightly different to most forums in that
it's more of a framework and almost *all* functionality is implemented
in Add-ons. This makes it very customisable. The add-ons are mostly
written by the main dev team, so they are all high-quality and stable. I
daresay someone has done an installer with the major add-ons already
built-in if you have a look around.

4) I use Wikipedia - it's very stable, well-supported, I've always found
it easy to install, and there's tons of support. Furthermore, it's
widely known, so people might "get" it more easily.

Cheers,

RB.