I understand that running a full node for Bitcoin is not like running a node for other altcoins that pay you a small amount, but I do have a question for the community.
Although I have never installed and downloaded all of the requirements needed to run a node, I have had the opportunity to walkthrough some wallets and also play around in mempool to see some unconfirmed transactions, and during that process I wondered if anyone running a full node can confirm any Bitcoin transaction in a block even if they do not receive the gas fee? Is it necessary for the transaction to be confirmed by a miner?
Full nodes check various aspects of a transaction, including its structure, signatures but it doesn't have to ability or control to pick the transaction to be included in a block. So running the full node will help you with the validation process quickly and broadcast the transaction to mempool which means they will be in the unconfirmed status.
Whereas miners are the one which involves in the selection of all the transactions from the mempool and include them in block they mine. They are incentivized to include a transaction with higher gas fee to earn those as reward for mining a block.