Troubleshot s/d and restart issue

I am fairly new to Mac. I bought a refurb 27" 2011 iMac a month or so ago. I am having issues with shutting down or restarting. Sometimes the iMac just won't do either. I have a 3 TB external HD formatted to NTFS so. I purchased and installed Paragon for OSX 11. Sometimes, when I click on that drive I get the spinning beach ball. If I do a comand-alt-esc and try to restart a non-responsive finder, it quits but does not restart. When this happens and I try to restart, the imac hangs on the gray screen during shut down.

Is there a way to troubleshoot this?

I was able to narrow the problem down to the Seagate USB hard drive. Whenever finder would lock up, I would pull the cable from the Seagate and everything was good again. I took your advice and copied everything from the 3TB drive to my iMac hard drive and another Western Digital Elements 1TB USB drive I had. Then I reformatted the Seagate to MAC OS Extended Journaled. Even after all of that the Seagate caused Finder lock ups even when I wasn't transferring files to or from it. On my Windows machine, it ran 24/7 with no problems. It must have a compatibility with Mac issue.

I did a work around by connecting the Seagate to an Airport Extreme and using it as NAS storage and for Time Machine. It's slow but at least it doesn't lock up my system now.

My iMac only has USB 2.0 (along with Firewire and Thunderbolt) ports. Can anyone recommend a good 3 or 4 TB USB drive that won't cause compatibility issues? Firewire and Thunderbolt drives seem very expensive.