Is this site a forum and if it is can anyone tell me this sites sponsors?
The question of how this site makes money was already answered here by me. In summary: English Language and Usage doesn't make money but it is instead supported by the sites elsewhere in the network that have ads, plus some things that are Stack Overflow specific.
Whether or not this site counts as a forum depends on how you look at it. The original idea for Stack Overflow (which is the oldest site in the Stack Exchange network of sites and shares the same format as this site) was that it is a hybrid of several things:
The big difference I see between this site and a forum is moderation. Questions must be on-topic and answers need to answer the question. There are even rules for comments. Users who gain enough reputation earn privileges which (among other things) enable them to moderate the site by doing things such as upvoting, downvoting, flagging, voting to (un)delete, voting to close/reopen, etc. There are also some moderators elected by the community (usually referred to as "diamond moderators" because they have a diamond next to their name) that have powers above and beyond what regular users get.
For example, just look at this question. Questions about the site don't belong on the main site, so a diamond moderator moved your question to the meta site.
If you have any questions about what I said, feel free to ask in the comments below this answer. Also, you may want to check out the tour, which explains the basics of how the site works.