Vendor select product category - front end

Hi I have a vendor setup and i would like for them to be able to select one of the categories when logged into the front end for their products, at the moment it looks like they can only publish products in a folder named after themselves. I would instead like them to be able to select 'books' for example and other categories if they apply but it looks like they dont have have access to select those categories?
(please see attached)

Also on the front end when i add a vendor it seems to create a category for that vendor automatically, does it have to do that, if i unpublish those categories does that affect the vendor? Ideally the vendor would use categories based around that the item is like on amazon, not based around the name of the seller.

Thanks Jerome, I shall have a read through all of this to make sure i understand it all as i did miss that bit!