Rekeying to smart contracts

General
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1

If I rekey an account to a smart contract, are checks like the ones below necessary?

Assert( Gtxn[1].close_remainder_to() == Global.zero_address()      ),
Assert( Gtxn[1].rekey_to() == Global.zero_address()                        ),

In theory, the smart contract has full authority over the accounts that have been rekeyed to it and no other account can rekey or close the account.

Is this correct?

2

It depends on the use case.
What is Gtxn[1] in this case?

But when you rekey an account A to a logicsig/smart signature contract account, then if the logicsig allows rekeying itself, then anyone can rekey A to the account of their choice and take ownership of A.
This is why in general you should always check that no rekeying occurs in smart signatures.

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