Anyone with parental responsibility, like parents and guardians, are able to claim childcare vouchers through their employer. 

You have to be employed and paying Tax and National Insurance. This applies to Company Directors also. In other words to make a saving you need to be paying tax, or would have to pay tax on any enhanced package

In the case of parents for instance, both parents can claim the allowance. It is per parent, not per child.

There must be no minimum wage issues if you take vouchers as part of a salary sacrifice scheme. Also note that at low levels of pay NI contributions can be a limiting factor