Google identifies popular nodes by itself. You can only remove nodes that Google lists. Your forum needs to become popular enough for Google to add SiteLinks.
Yep; there is nothing you can do except have a lot of threads that the algorithm considers relevant to the search query
For eg, see this search result: https://www.google.com/search?q=xenforo+spam
It also depends on how you search for a specific forum or information about that specific forum or its content. See below for the search results on my forum, I search for information about that type of forum and then the actual forum name and get different looking results.