The second part of your question on "Does the thyroid die off and is it still part of you," answer is:
The RAI is designed to kill off the thyroid either in total or to leave a part of it functioning. If you receive a small dose some of the thyroid will stay alive and active producing hormone.
If you receive a larger dose, then the thyroid is killed off and will decrease in size due to atrophy. It will never go away, it will simply be non-functional.
Example, I had RAI. Later I had to have two parathyroid removed, (NOT related to Graves’ disease) I asked the surgeon to remove any remaining thyroid in there since I was to be opened up anyway.
After the surgery the surgeon told me the remaining thyroid had atrophied ( shrunk) to the point it was not worth the bother to removed the dead tissue, it was causing no harm so it was left in.
This is the reason we go on replacement hormone to give our bodies the hormone that the thyroid used to provide. I hope this helped to answer your question.