Can miner pay transaction fee with coinbase (if maturity is disabled)? If I understand correctly,


the first transaction in a block may collect transaction fees (difference between inputs and outputs) from the following transactions in the same block; and
subsequent transactions may use outputs from previous transactions in the same block.


If the block maturity check is disabled, so that newly minted coins may be utilized immediately, can a circular dependency of transactions arise, i.e., a miner uses coins generated from the coinbase to pay for transaction fee of a transaction in the same block, but the fee is then returned back to themselves (collected by the coinbase)?
If your altcoin removes the maturity check, I don't see why not. The only prerequisite would be that the fee for the transaction spending the coinbase input must be decided before building the tx, which isn't very hard.