with bitcoin, no. however, if you lock your BTC into payment channels on the lightning network, you can collect fees when your node is used to route transactions. fees are much lower than on bitcoin's blockchain, though. so unless you're a very well-connected node, you probably won't make much in fees.
He retains control of his transactions, and this could enable him to save a bit on fees.
you don't necessarily need a full node for that. lightweight nodes (like electrum or mycelium) and even online wallets like blockchain.info allow you to manually set lower fees. it's third party services like exchanges that really screw people on fees.
