As for a dominate spell, here is the description in the SRD (p 137):
While the target is charmed, you have a telepathic link with it as long as the two of you are on the same plane of existence. You can use this telepathic link to issue commands to the creature while you are conscious (no action required), which it does its best to obey. You can specify a simple and general course of action, such as “Attack that creature,” “Run over there,” or “Fetch that object.” If the creature completes the order and doesn’t receive further direction from you, it defends and preserves itself to the best of its ability.
You can use your action to take total and precise control of the target. Until the end of your next turn, the creature takes only the actions you choose, and doesn’t do anything that you don’t allow it to do.
This would clearly enable the caster to force the dominated person to answer a question. As a matter of gameplay, how would we work out whether or not the person knows the answer? I would have thought the canonical way is by making a knowledge check.
Another way to look at it is this: the caster instructs the dominated PC to answer a question. The player now has to have his/her PC obey that command. But what does the PC say? If it is certain that the PC knows the answer, the answer has to be given. If it is certain that s/he doesn't know the answer, the PC answers "I don't know." If it is uncertain, a check is made. But who has authority over the question of whether or not it's certain or uncertain? The GM (per SRD p 77).
What makes you think that the
player has any say over this?
