Why not keep it simple and use Sync? https://support.mozilla.org/en-US/kb/how-do-i-set-sync-my-computer

Tried to set up, but after uninstalling Firefox on new machine, I downloaded new install file because I thought I would get a new profile, but it wouldn't run. Said couldn't find profile. Repeated attempts got a "Somethings wrong" message. I had used "about:profiles" to create a new one and loaded the individual files (not the file title) into it. Made it the default. Then Firefox wouldn't run. Could I get into "about:profiles" the MSEdge browser? How would I correct?

If you want to transfer a profile to a new system, it is best suggested to use the sync as jonzn4SUSE (jonzn4SUSE) mentioned. What I doubt would have happened is that along with the profile file, the data file that opens that particular profile must have been deleted. I suggest you to turn on sync in your old system, then, try uninstalling the complete FF in new system and reinstalling it.

I did uninstall and reinstalled, but Firefox didn't run. Tried to load, but displayed error message as previously noted. Should I try again? If able to do Sync, can I then select the external hard drive as a source?

That is likely because the profile folder you copied isn't registered in the Profile Manager (profiles.ini).

See "Profile was moved or renamed":

• https://support.mozilla.org/en-US/kb/how-run-firefox-when-profile-missing-inaccessible

Firefox uses two locations for the Firefox profile folder. One location for your personal data (e.g. bookmarks) and another location for temporary files like the disk cache, so make sure you copied the profile to the correct location.

Location used for the main profile that keeps your personal data (Root Directory on about:profiles).

• C:\Users\<user>\AppData\Roaming\Mozilla\Firefox\Profiles\<profile>