Issue #1: I am running into the problem of saving metadata
Does this only happen with DNG while and happens only when you save to External drive?
I would recommend you to check External drive Read Write Permissions again.
Issue #2 : At times when I need to create a LR catalog containing multiple projects (multiple LR catalogs) that are saved separately on my external drive, I run into the problem of LR not reflecting some of the metadata
Did you also tried resetting Lightroom Preferences once(backup your catalog Lightroom5 catalog.lrcat before resetting) Recover catalog and images after resetting preferences
Thank you, Akash. I think I may have answered my own questions.
I was still working off of a "ghost" catalog on my desktop after having moved my files to an external drive. Although I relocated my original files on the external drive (originally located on my desktop where I created the LR catalog) in my original LR catalog, it seemed to have thrown off LR somehow and some of tagging and flagging wasn't reflected. So, I moved the LR catalog to my external drive as well and reimported it in under a new catalog but it was still giving me the same issues. Next, I played around with the permission on my external, which seem fine. Finally, I threw my hands up for a couple of days after LR was doing all kinds of wacky things in the background with my moved files (secretly praying it doesn't delete anything...).
Can't explain it but after 2 days of taking all my old LR catalogs off my desktop, I started a fresh LR catalog again and used "Import From Another Catalog" to bring in the projects I still needed to put final touches on. Well, this time, it worked like a charm. Not sure why all the issues before, but I hope this helps anyone else out there that may run into this struggle. Thank you for your reply.