Hi, great questions. Answers as I believe them...

1. What are the ramifications in England of a gun "failing proof"?
You can't sell or use it legally.

2. Does that mean it can't be legally sold?
Correct. It is illegal to seel such a gun. Gun Dealers can hold them though.

3. Does a seller have to refund the purchase price?
Almost certainly. But not sure on legal ramifications. Dig or Toby, someone else is sure to give you a proper answer.

4. What if it was purchased at auction?
It is illegal to sell a gun at auction out of proof.

5. Can the owner legally shoot/hunt with an out-of-proof shotgun?
If you own it yes. At your own risk. Guns fall out of proof through normal use.

6. Would a hunt club or public shooting range prohibit its use?
How would they know? smile