Can women contribute or ask questions using a microphone in a program where there are men?

Praise be to Allah, the Lord of the World; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.

There is no harm for a Muslim woman to participate in useful T.V/Radio programs, especially if religious in nature from which she may benefit both in worldly and religious affairs. A woman's voice is not Awrah (i.e. we are not prevented from hearing it).
Allah Says (interpretation of meaning): {… And when you ask (his wives) for anything you want, ask them from behind a screen, …} [33: 53].
Another verse indicates that only "Being soft in speech" is Haram, not the speech itself.
Allah Says (interpretation of meaning): {… then be not soft in speech, lest he in whose heart is a disease (of hypocrisy, or evil desire for adultery, etc.) should be moved with desire, but speak in an honourable manner.} [33: 32].
But, if a listener may fear temptation of a woman's voice or he may get pleasure from hearing her, then it is Haram (for him to listen to); otherwise, it is not.
Allah knows best.