Can an adult grant power of attorney to a minor and be bound by contracts signed by the minor on his/her behalf?
In the US, a minor generally cannot enter into a contract and thus is ineligible to be given a power of attorney.
There are no special qualifications necessary for someone to act as an attorney-in-fact except that the person must not be a minor or otherwise incapacitated. The best choice is someone you trust. Integrity, not financial acumen, is often the most important trait of a potential agent.