All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
A vow is defined as a commitment of a Muslim who is competent for religious assignments to do a particular act of obedience that is not obligatory on him before making that vow. Khaleel said:
"A valid vow is made when an adult Muslim who is competent for religious assignments commits himself to do to do a particular act, even if it is made in a state of anger … A vow is considered binding and valid when the person makes a vow to do an act that is recommended in all cases and times."
Therefore, making a vow to give one's child a religious education should be fulfilled.
As for your second question, the vow is interpreted according to the intention of the vow-maker. If you intended to give your son a formal education beside the religious one, then you may do so. However, if your intention was to give him a religious education only, then it is impermissible for you to direct him to any other kind of knowledge, except those fields of knowledge that are essentially needed for Islamic studies, such as Arabic grammar, morphology, semantics, rhetoric, and mathematics. As for your third question, the answer is that if the vow-maker is unable to deliver on his vow, then he is obliged to offer expiation like that for breaking an oath. However, in your case, you vowed to urge and direct your son to acquire religious knowledge, and being unable to do that is unlikely, unless your son was lost and could not be found, Allaah forbid.
Allaah Knows best.