Q: MacPro1 to External to MacPro2 file issues

This is driving me nuts, and costing lots of time... I have a MacPro 2009(A) at home, a seagate 2TB external for carrying files, and another MacPro 2009(B) - the issue is: about 50% of the files I copy to the external HD have limited access and can't be open, modified, and resaved while still on the external. These files have "read only" under Sharing and Permissions for "staff" and "everyone"... but it's not on every file I put on there. Files packaged from AdobeCC have this limited access, and files copied from desktop on MacPro 2009(A) have it, but not files copied from MacPro 2009(B).

Copying files from the external HD to an internal HD removes the "read only" on single files, but does nothing to files with folders copied the exact same way???

What do I need to do remove these limitations 100% from all files, no matter where they are, or how they were saved to whatever device. I have so many duplicate files now I'm about to go insane (I've generated 4,789 files in the last 3 months - many are duplicates, I work 2 jobs, 13 hours a day, and have to find a solution)

Thanks in advance. Rick