Is it permissible to increase the tuition fee for teaching the children to 75-80% of the market rate without informing the father, whether for subsequent hours only or for all hours?

First: If the lease agreement does not specify the rent, and the young man studies for a wage, then the lease is valid, and he is entitled to the customary rent (اجرة المثل). If he wishes to waive some of his right, there is no harm in that. However, an increase beyond what his peers receive is not permissible except with an explicit agreement.

Second: It is not permissible to combine a lease agreement with a loan (سلف); this is due to the Prophet's prohibition (peace be upon him) of combining a loan with a sale, and a lease agreement is a sale of usufructs. The majority of scholars prohibit combining a loan with any commutative contract. If what he received was an advance payment from the rent, there is no objection if the rent was known. Otherwise, what is in his possession is a trust (أمانة), and if he benefits from it, it becomes a loan.