Can A Mining Farm Profit From Transactions
Fees only get created by the individuals creating the transactions. There is no way for a miner to take a fee from a transaction that did not include a fee. Miners can be selective if they choose to and only include transactions with fees. 

Essentially the answer to your question is no they cannot gain any advantage over any other miner. They can select and include transactions with fees but this can be done by all miners.