I don’t think they are “surrendered”. They are turned over to the experts and they go through it. If the find is not considered “historical” or worthy of study, museums, etc. the finder can keep it. If it is worthy, the government pays the finder. I thought the government had to pay the entire estimated value of the find, but this article says “a portion”.
The treasure laws in England are pretty good - promotes metal detecting to uncover their history. I looked into trying to do it in my state of Washington. Lots of various laws and regulations trying to do it in parks, beaches, etc. (Stupid laws - no wonder nobody ever finds Roman coins on the beaches of Puget Sound!)
You are correct.
The government determines who keeps the find.
I’m not sure how a value would be fairly established however...