(a) That's right. In addition to being liable to pay a reasonable price for goods or services that are 'necessities', a minor has the capacity to be bound by a contract for employment, an apprenticeship, training or education, as long as such agreements are, on balance, for the minor's benefit.
In the example, the proposed contract for singing lessons would clearly fall within the concept of a contract for training or education. Such agreements do not have be considered a necessity to be legally binding - it is enough that they are substantially of benefit to the minor. If the agreement is not substantially of benefit to the minor, it will not be enforceable against them.
Note: If a minor (or other person who lacks full capacity to contract) has received things from a supplier that the minor is not contractually bound to pay for, they may nevertheless be required pay a reasonable amount for what they have received. Otherwise, they would be unjustifiably enriched.