Can I keep all postings private?

Only people who you gave the password to could access password protected forums. This includes search engines who would also not be able to access those forums.

However, instead of password protecting forums, I would suggest using the forums permission system instead so that only certain groups can access your private forums. You can then check out members and place them in different groups so they can then access your private forums.

By using the permission system you can also hide forums that people can not access so that they remain completely invisible to all except those placed in the groups that can access those forums.