Am I obligated to pay the remaining amount to the barber, knowing that he insisted on providing additional services that I did not request or desire, and I did not find the remaining amount available afterwards?

This transaction falls under the category of Ijara (leasing/hiring), and it is a condition therein that the rent/fee must be known, as Ibn Qudamah stated: "It is a condition for the consideration in Ijara that it be known." So, if the inquirer agreed to the barber's offer and said nothing, this is considered an acceptance and satisfaction with the offer. If the fee is unknown, then the contract is invalid, and the Ajrat al-Mithl (customary/market wage) becomes obligatory if the benefit has been utilized, which is what experts estimate.