I would like to be able to set up access levels to certain categories where the public can read and view all the posts, but needs to register in order to write a post. In the forum advanced configuration I am not seeing how I would set this up. It seems I cannot give the public view access without giving them posting rights. Am I correct on this? Can somebody tell me how I can set it up so that the public can only read and not post unless registered?

Not natively possible. You'll have to use a third party add on like GroupJive, that seems to have problems with the Default Ex template, or user supplied hack. Doesn't look like the next version will answer the almost 1+ year old promise of group access levels.

2.0, rebuilt from the ground up, should be available this fall and have all those features. But then again FireMessage was promised early this year.

This isn't very difficult:

Go to your Fireboard Configuration and then to the Security section by scrolling down.
In the security section, the first and the 3rd option should be on "no".

If the first option is on "yes", this means that only registered users have access to all of the forums. They won't even be able to see what the forums are called.

If the third option is on "yes", this means that everybody that has access (see above) to the forums is able to post on them. If this is on "no", only registered users are allowed to post.

So putting them both on "no" should solve your problem.
It worked for me too (I'm using FB 1.0.4 Dutch Stable).

Good luck!

BioHazard