When you're being sued, the first thing to remember is that it's basically designed to be a logical process, and if you get wrapped around the axle emotionally, then you're almost certainly going to lose, because you'll be focused on the wrong stuff and will miss that which is really important.
Ok, are they entitled to make you answer a bunch of dam'fool questions? Probably. It depends on what court you're in, and in what state. Interrogatories are questions directed to a party as part of the "discovery" process. Discovery is designed to help each side prepare for trial. You can send the plaintiff discovery, too, including Requests for Admissions, Requests for Production of Documents, Interrogatories, and you can depose the plaintiff or other witnesses, as well as interrogatories of your own.
The lowest level of trial court usually doesn't have a provision for discovery. Most states, in my experience, have two levels of trial court, there's a "court of record", often called the Circuit court (Supreme Court in N.Y.) in which all the really important, big-money civil cases are tried, as well as criminal cases for things like
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, robbery, and murder. The lower court usually is not a court of record, and they deal with the traffic tickets, misdemeanors, preliminary hearings, landlord/tenant stuff, and smaller dollar value civil cases. There is always discovery in the courts of record, almost never in the lower courts. So, look at the first piece of paper you got served on you, it should have some kind of paperwork attached with a signature of a clerk of court or deputy clerk. The name of the court will be on that paper. Call the clerk's office for that court and find out if it's a court of record (and anything else you're curious about, for that matter, keeping in mind that they're not lawyers and cannot give you legal advice). Then, see if you can find out on the internet whether the rules of civil procedure permit discovery in that court. I suggest going to court and watching a day of trials and hearings in cases like yours - you may see a sympathetic lawyer (i.e., one who represents defendants) who'll tell you what's what for free in the hallway after a hearing (if he blows you off, just ask another one).
You almost certainly have a limited amount of time in which to prepare and file a written response to the plaintiff's initial pleadings; and if you don't do it, that's going to give the plaintiff a slam dunk.
Btw, file a motion for monetary sanctions against the law firm - if they filed suit against the wrong person as a result of a failure to figure out whom to sue correctly, that's a waste of your time and the court's time, and the citizens' tax dollars. You lose time from work, have to hire a lawyer (you really, really should, you know), you're entitled to recover all that back. If you take active steps to defend yourself promptly, on the theory that they're suing the wrong person, they'll almost certainly back off pretty quickly.
But the simple answer is, you probably do have to answer the interrogatories. Remember that you don't have to be right to sue someone. Anyone can go down to the local court house and sue anyone at anytime for any reason (of course, if it's a bad reason, there's always sanctions). It's up to you to defend yourself and if you fail to do it, then they can get a default judgment and you'll have to pay it. You can protest the injustice of it to the high heavens, but you'll pay that judgment. Btw, in most courts, you can't get a default judgment against someone for a failure to answer interrogatories, but you can get them held in contempt for failure to respond, and one of the sanctions available in that case (aside from a small amount of jail time) is summary judgment.
Please, please, please, find a good trial lawyer who defends people in civil cases (other than an insurance company defense lawyer) and buy half an hour of his/her time (the appropriate pronoun for me, btw, is "he"), to get some straight stuff about your situation. (Hint: If you call lawyers who do personal injury work in your area, and ask them whom they'd hire to defend them if they were sued for the debts of another person, after a while, the same two or three names will keep coming up. Call one of those two or three attorneys.)
My email address is available, you can click one of the three icon things at the bottom of the message, or the "author's kit" thing on the upper left, if you like. Anyone can feel free to email me; after all, the worst that could happen is that I might choose not to reply. And, of course, I can't practice law outside of Virginia (although I am admitted to practice in the U.S. Fourth Circuit Court of Appeals and the U.S. Supreme Court, which sometimes takes me outside of Va. - one time I had to drive to South Carolina for a hearing before the 4th C., because that's where they happened to be sitting on the day my hearing was scheduled. What a pain. Lost on that one, too. And I usually tell people I don't go to court South of Petersburg, Va.)
****Adult term removed - Jason