We have some threads that we don’t want newbies to be able to post on. Is there any way of restricting who can post? (Like, maybe, to members at level 2?)
Yes, just amend your Security Settings for the Category, e.g.:

In this example, TL0 (ie anyone who has an account) only has the ability to see but not post here (unless they are also at least TL2).
Thanks! And can that be specified by discussion category? Or does that setting apply then to all discussion categories?
Specific to a Category.
Perfect, thank you very much.