Turn TDE off when restoring SQL databases
But specifically, I am wondering how to restore from a TDE enabled prod environment to a TDE enabled non-prod environment.


There is an entire Docs article on this. Let us know if you have specific questions.


  Once a TDE database is restored over without TDE being turned off, is it using the source server's keys going forward?


You'll see, in the article above, that yes you won't be able to read the database unless the server certificate which is protecting the database encryption key (DKE) which resides in that database has been restored and available on the destination server.


  I am wondering if turning TDE off and on (which would take hours) would be a requirement in this situation.


If the customer can't use TDE, then it's a requirement (Non-Enterprise Editions). If you don't want to send them your internal certificate, then once restored to the destination server, rotate the server certificate to a new one. It won't require any extra operations (apart from metadata changes) on the database. you could then send the customer the cert + the database, in two separate communications channels or a secure channel, of course.


  Also note the strange behavior when I restored below. It appeared that it is carrying a historical key through a previous incarnation of the database, and when copying to a server with the same database name, is allowing the second server's key.


Huh? Your output doesn't show anything but the encryption state of the database. You quite literally can't restore the database without the server certificate. So if it let you restore the database without any issue and you didn't restore a server certificate for it, then the logical conclusion is that the current server certificate is the same on the source and destination server, which is a security no-no.