So I ran the duplicate file program, and it found almost 14 megs worth. At least 2 of each duplicate found. For example:
File:                              Folder: Size: Duplicate of:
Minutes of Meeting 40 beta (1).png (folder) (size) Minutes of meeting 40 beta
Minutes of Meeting 40 beta.png     (folder) (size) Minutes of meeting 40 beta (master)

Before I remove all these duplicate files that have been found, I want to be sure that PM is keeping an original, or do I need to delete just one of these?

How do I know which ones to delete, without causing a crash, or program failure?

PMP has always left one copy of each file when I have used it to remove duplicates. I avoid deleting exe and dll files as these are most likely to break an application.
There’s always a chance that something will go wrong though. It’s usually my fault when it happens to me. I can’t stress enough how important it is to have a current backup of your machine and any storage. If you don’t, I’d suggest you avoid deleting anything unless you are absolutely certain. Even if you don’t use utilities like PMP, something will break your device at some point and you’ll be glad of the backup. Storage cards don’t last forever and PPCs crash more often than we’d like. My HD2 had a ‘moment’ just this week, but, thanks to Sprite, I was up and running in 20 minutes. There are other backup programs and there’s even a free application that will back up your PIM databases.