Which forum script has blog in them?

[zeus]

Most paid forum scripts has it. In the free ones, blog can be added but certainly you have to work for it.

Exactly correct. Can be done but it needs special treatment. And also the user have to have some experience in programming.

Currently, I am looking in phpbb but they doesn't offer much help in integrating a third party service. And also so I checking mybb and Smf too.

As I said earlier. Mybb provides. If you can't find any links or information then contact them directly through their community forum. You don't have to be a user of mybb to ask for help.