Catagory output template?

Hi,

We have categories output from a menu link. we want to understand how to do 2 things:

1. Get rid of the “Category: whatever” txt on the top left

2. The output of the categories page looks to have a right side block area, yet we were not able to get a widget to appear in there. We are stumped as to what widget area allows you to put blocks in this page? we either need to find out how to put blocks in that page, or just turn that off or make it full width. There is just no page layout options like a normal page.