If you capture a foe and cast dominate person on them, will they then truthfully answer any questions you ask them, such as where their base is located, what secret entrances it has, the password of the day, and so on?
I think you could.
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.”
Since you are charming the creature and it follows your instructions, but appears to still be conscious and aware rather than a mindless slave, I think that you could ask it questions and it would answer them as to the best of its ability. Its up to the DM whether it tries to please you and be helpful or is only compelled to meet the minimum of the request.
The answer is without a doubt YES
Don't overcomplicate this because it's really simple. A person under the effects of dominate person WILL do it's best to obey any command given. If that command is to answer all your questions with complete honesty, then that's what they will do.
I just did this in my campaign, while the "Charmed" status is used in Dominate Person, you have to look at the additional language in the spell. First off Charm Person is a 1st level and Dominate is a 5th level so it has MORE.
1st part. 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.
This is no longer a verbal conversation everything is now in the mind of the Dominated. So the question becomes what does having a telepathic link entail. For that the only place that details a telepathic link is the telepathy spell. Yes its level 8 but it lasts 24 hours.
Telepathy spell -
Until the spell ends, you and the target can instantaneously share words, images, sounds, and other sensory messages with one another through the link, and the target recognizes you as the creature it is communicating with. The spell enables a creature with an Intelligence score of at least 1 to understand the meaning of your words and take in the scope of any sensory messages you send to it.
So this is the level that the interrogation takes place. No longer can you hide behind saying nothing because you can't stop thinking. Even if you attempt to think about other things and hide your thoughts the 2nd most important part of dominate person comes into play.
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.
So, yes it has the "Charmed" Effect but that is just the tip of the iceberg to being interrogated by Dominate Person.
From the wording on charmed,
A charmed creature can’t Attack the charmer or target the charmer with harmful Abilities or magical effects.
The charmer has advantage on any ability check to interact socially with the creature.
The takeaway from this is that while concentrating on Dominate Person, you would have an easier time asking for it.
You attempt to charm a humanoid you can see within range. It must make a Wisdom saving throw, and does so with advantage if you or your companions are fighting it... The Charmed creature regards you as a friendly acquaintance. When the spell ends, the creature knows it was Charmed by you.
Charm Person explicitly says that the target regards you as a friend. While charmed in this manner, the target would likely volunteer the information, rather than being probed for it.