Hi Jason, welcome to the forums.
It is possible to assign things like knowledgebase, download and troubleshooter
categories to what is called
template groups (what you appear to be describing as companies). A different template group can have a completely different theme, style and categories for the aforementioned items.
You can read more about how this system works in the Administrator Control Panel section of the SupportSuite manual, which is not yet finished but all of your questions are covered (
http://docs.kayako.net/supportsuite).
Also, please note that you cannot share your SupportSuite licence with different companies in the way you are describing (what we call support desk sharing or hosting) - you may only use it for your own company (up to) with the possibility of using it on different fronts.