What restrictions are placed on the header by ASICs?

[TierNolan]

What restrictions does mining hardware place on the Bitcoin block header?

Can you give mining hardware any 80 byte header and it will search it (updating the 4 nonce bytes and maybe the timestamp)?

Does the version field have to be positive?

Does the difficulty target have to be a reasonable value?

Does the previous hash have to have at least 32 zeros?

Does the merkle root have to encode at least a coinbase for the extraNonce?