How do I delete a category and move all the posts?

Is this even possible?

You can move forums from one category to other via Admin Panel, Content Admin -> Forums panel.

If you want to move them to a different, exiating forum, you'll have to do it manually, one by one, using the admin option available to you. If there are many, you might need a database hack but I do not have time right now to explain that one to you. It needs to be custom made.

How can I move the posts from one category to another? I just see that i can edit the categories or delete them.

You can't do that from the admin panel.

In the bottom of each thread there's a drop-down called 'Moderator Options'

From the drop down list, select 'Move thread'
Then choose what forum to move the thread to, and hit the [Move Thread] button.

You'll have to do this with all the threads you want to move.

When all threads are moved, you can go to admin panel and delete the category.

Or better use ExtBoard, in the Moderator Panel you can move multiple Threads or in ACP you can select where to move posts when deleting a forum.

Where can I get ExtBoard or ACP?

Thanks

ACP = Admin Control Panel :)

ExtBoard you can get -> here
Note, its designed fro advanced users or users with php-knowledge