Praise be to Allah.
Calculating tutoring fees
If there was agreement on the work to be done but no mention of the fee, and this young man is known to tutor in return for payment – as appears to be the case – then the hiring contract is valid, and he is entitled to the going rate. It does not matter what the young man intended to charge.
It says in ar-Rawd al-Murbi‘ (p. 410):
“If a person enters a public bath or embarks on a ship without an agreement on a fee, or he gives his cloth to a dyer or tailor to work on it, without an agreement on a fee, that is valid, on the basis of the usual going rate, because what is known to be the going rate is as good as stating the rate. The same applies if he gives his goods to someone to sell them, or he employs a porter to carry them, and the like. The worker is entitled to the going rate, even if he does not usually charge a fee.”
If he wants to give up some of his dues and take less than that, as a favour to the father of the student, there is nothing wrong with that. As for increasing it above what tutors usually charge in his city, that is not permissible without the express agreement of the father of the student.
Combining hiring and giving a loan: Valid?
It is not valid to combine hiring and giving a loan , because the Prophet (blessings and peace of Allah be upon him) said: “It is not permissible to arrange a loan combined with a sale.” Narrated by at-Tirmidhi (1234), Abu Dawud (3504), an-Nasa'i (4611); classed as sahih by at-Tirmidhi and al-Albani.
If what is meant is that the father gave him payment in advance, there is nothing wrong with that, if the fee is known. But if it is unknown and the contract is invalid, then what he has in hand is like a trust, but if he uses it, it becomes like a loan.
And Allah knows best.