Can you fight a summary of judgement claim if you didn't initially answer the plaintiff's interrogatories that were mailed to you?

Yes, you can opposed (fight) a summary judgment claim (motion) if you did not answer the person's interrogatories that were mailed you. The way to oppose such a proceeding is to create a "triable issue of fact" so that the matter can go to trial before a judge or a jury.

The way to do so is to submit a declaration under the penalty of perjury contesting material issues of fact. A summary judgment motion is complicated to bring and oppose. As such, I recommend that you consult with an attorney who does civil litigation to assist you.