When we execute a function on a smart contract, the transaction will be verified by all miners in the entire network before being written to the blockchain. I want to know no matter how complicated the smart contract function called by this transaction is or the function needs to pay some fees, do miners have to execute this function for verification?
For example, the function on this smart contract needs to pay token to call the payment interface on chainlink.
The transaction will be included in the blockchain the moment it is included in a block (at least from the miner's perspective), so it doesn't need to "wait" for other nodes to verify it first. If the miner is dishonest and the transaction result is not calculated correctly the block will be ignored by others.
Miners can choose which transactions to include in their block and they can even mine empty blocks if they want. Typically they simply include the transactions which provide the biggest benefit to them (the ones with the hightest gas price). This is the reason transactions with high gas price are processed faster.
So it is possible that a transaction is never mined by anyone. Also it is possible that nodes choose not to verify an incoming block and simply accept it, but this shouldn't be the case typically.
