Displaying Category Post

Hi all,
I am trying to revamp our current static website into WordPress and am really new to WordPress so I hope this is an easy question. I have searched the forums and found similar questions but none has quite answered it. What I would like to do is have several categories for post, such as News, Reminders, Notices, Upcoming Meetings etc.. I want the recent post for each category displayed on the right column of every page (using the Designfolio theme). However I want to have a seperate widget/divider for each category. This way when I post something under upcoming meetings, it only shows up under that divider. I had it sort of working but it seems that the post show up under multiple categories, even if I marked the post to be one specific category.

Also, can I link a post title to a file? I would like to post dates under the upcoming meetings category, when someone clicks on the post, it would open a pdf of the agenda instead of going to a page for that post…hopefully this makes sense.

Thank you in advance for any help.
Chris