No, it wasn't free.
Eklavya, who possessed the art of archery (Dhanusha) from Drona by virtual means, also was held responsible to pay it by giving away his thumb.
Then Drona, O king, addressed Ekalavya, saying, 'If, O hero, thou art really my pupil, give me then my fees.' On hearing these words, Ekalavya was very much gratified, and said in reply, 'O illustrious preceptor, what shall I give? Command me; for there is nothing, O foremost of all persons conversant with the Vedas, that I may not give unto my preceptor.' Drona answered, 'O Ekalavya, if thou art really intent on making me a gift, I should like then to have the thumb of thy right hand [Adi Parva]
Drona also took the 'fees' from Kuru-s.
Drona thought the time had come when he could demand the preceptorial fee. And, O king, assembling his pupils one day together, the preceptor Drona asked of them the fee, saying, 'Seize Drupada, the king of Panchala in battle and bring him unto me. That shall be the most acceptable fee.' [Adi Parva]
in Santi Parva, Bhishma suggests that the fees should be given to those Brahmana-s who are in need of it. Others can be given the [Guru] Dakshina:
... to discharge their obligations to preceptors and the Pitris, and pass their days in reciting and studying the scriptures, wealth and knowledge, O Bharata, should be given. 1 Unto those Brahmanas that are not poor, only the Dakshina, 2
1 In India, from the remotest times, preceptors are excluded from charging their pupils any fees for the instruction they give. No doubt, a final fee, called Gurudakshina, is demandable, but that is demandable after the pupil has completed his studies. To sell knowledge for money is a great sin. To this day in all the indigenous tols of the country, instruction is imparted free of all charges. In addition to this, the pupils are fed by their preceptors. The latter, in their turn, are supported by the charity of the whole country.
2 Dakshina is the present or gift made in sacrifices.
And there is nothing wrong in it. If a student learns any art from a teacher, then he becomes indebted (Guru runa). This debt was usually paid by Guru Dakshina, in earlier times when physical currency weren't famous. Moral debt is the most costly thing & hence Kshatriya-s or any self-dignified person should never carry that.