Is it permissible for a sixteen-year-old boy to greet a foreign princess (who is not a mahram) in order to receive a valuable award, given the difficulty of avoiding it?

There is no harm in attending the ceremony and receiving the award from the stage while lowering your gaze. However, do not extend your hand to shake a woman's hand, and inform her that you do not shake hands with women, following the example of the Prophet (peace be upon him). If she does not give you the award, then leave it for the sake of Allah, for whoever fears Allah, He will provide for him from where he does not expect.