Category specific templates

Hi.. I am trying to wrap my mind around a WordPress build and was hoping someone could help give me some direction in how to achieve this..

I am building a site where the nav is going to be mainly driven by what category the posts fall in. A couple of things I am trying to understand..

How can I have the previous/next links stay within a chosen category ?

Is it possible to show a calender that only highlights entries that have fallen in that specific category?

Thanks for any assistance with this.