I think installing PostFix solved my issues, but it seemed *too* easy

Generally speaking, I find postfix to have pretty good settings out of the box. If you're concerned about other people abusing it, run it through abuse.net's relay testing, which should answer #1.

2 - that depends on how others have their spam filters configured, but you should be fine. You could test this by signing up for & sending to a few free accounts (Hotmail, Gmail, and Yahoo will cover most of the mainstream configurations, including DKIM, SPF, Postini, etc)

3 - You haven't missed anything major that I can think of off the top of my head... I'd say just test the heck out of it, watch your logs for the first week, and you should be good to go.