1)See you at the forum. ==> at + location
2)Let's discuss in another forum. ==> discussion is held in an enclosed area, say meeting room. Maybe 'at' could also work here.
3)I'm on the forum. ==> ???
4)I've logged on in/on the forum. ==> ???
5)This is similar to the question in/at the Delphi Forum. ==> ???
6)Have you post anything on/in the forum recently?
7)I've read some good posts in the forum. ==> Here, I htink forum functions as a mass media, for example, advertisement in the newspapers.
'on our teams' comes from on our team roster, but it doesn't necessarily have to mean 'on the roster'. Both 1. and 2. share the same meaning: belongs to our team. 'in our team' means, belongs to (from inside, within).
To add to tdol's reply :D , in North America, 'on our team' is used both in Sports and in Business.