As Karla mentioned, Google Analytics can be helpful in this regard, but it's better for tracking the activity of users on particular pages in the community. Tracking forum usage in terms of topics created can be done in the Content area of the Social Analytics beta feature. It can track content creation by particular Groups of users, such as the members of a particular Space, and can also check forum usage on a per Space basis, so you can see which spaces have the most active forum channels. It does not check them for individual channels in the visualizations, but the exported report can isolate that information.
Regarding time to first comment and time to closure, I'll pass those on to our Product Development team as possible feature enhancements to our own reporting functions.