After attempting to check for the software update, the red and blue arrows
in the top left as well as Device Management connecting to DM server stuck
in my notification center for over 8 hours now. Anything I should/can do with the
phone or just wait it out?
Have you downloaded an app that monitors or restricts your data usage?
I had been having this issue for the last few days, "connecting to DM server" with the blue and red arrow icon appearing every 30 seconds or so, and found that my Onavo app identified "Device Manager" as a data hogger was blocking the phone from checking for software updates via mobile data. I went into Onavo settings and updated to allow the program to use mobile data (it was restricted to wi-fi), then went to my phone's settings and searched for a software update.
Even though the phone did not have any updates, this seems to have solved the issue. Its been about an hour now without the icon showing up.