When the media is Imported, it will show the Protection as calculated from time of backup. So, for example, If you set protection to 4 weeks, and 10 days later, you exported teh media and imported, it would show protection of approximately 18 days (4 weeks = 28 days -10)
If you imported the media 5 weeks after backup, Protection woud show as Expired
The Protection attribute is set in the Section Headers as they are written to the tape as the Backup runs. When media is imported, those attributes are read, and the IDB is updated
I'm not sure of what you are asking here
"Now, when I export/import the tape again, will I see Data protection set to Permanent without writing the tape?"
but, once you have set the Protection on the session, it does not matter what it is set to on the tape, because it is not the tape that is being protected, it is the session, and its protection that either allows the tape to be reused if Protection has expired, or prevents teh tape from being reused if Protection is still intact