Again, I would like to allow an installation with an fixed/embedded product key for any and all machines. Once that key expires on a given machine, the user must provide a paid for product key. Is this scenario supported?
Yes, but you don't need to embed a product key (or a trial extension). TurboActivate already handles trials out of the box. That is, even if the user uninstalls and reinstalls your app the same amount of trial days will be used. So you don't need to bother the user with trial extensions or trial product keys. Just use the trial functionality built into TurboActivate for prospective users.
If a user wants to try your app for more days (for any number of reasons) then you can give the user a trial extension.
Does this make sense?
After the product key expires, the user uninstalls and obtains a fresh product key and reinstalls. Is there anything built into the licensing framework to prevent this?
If you use the trial functionality built into TurboActivate then the user can't restart the trial just by uninstalling and reinstalling your app. You can always send the user a trial extension if they legitimately need more trial days. But even then they can't use the same trial extension over and over again.