No. It it not.
Nonce is for injecting variability into the block header so that the resulting hash value can be modified without needing to modify any of the transaction data.
Incorrect.
Current value for block hash difficulty target is set to create around 10 minutes delay for block creating.
Clearly.
Miners. Miners keep trying a different nonce until they either find a solution or run out of nonce values.
4 byte integer.
I just did.