When you sue someone you are entering into the big league. You are exposing yourself to vicious lawyers that will do and say anything to hurt your case, its what they are paid to do.
Rules surround depositions are very loose. Opposing counsel can ask you just about anything and your lawyer has very limited ability to object or stop certain questions from being asked. However, he should object while those questions are being asked to possibly prevent those answers from being brought into a trial.
I was deposed about a month ago and in the beginning my hands were clammy and my heart was racing. However, I knew what counsel wanted out of me and I wouldn't give it to him. He spent two hours asking the same question with no avail. My best response came at the end when he asked "don't you feel at least partially responsible for the accident." Well, it would be easy to say "yes." But instead I said, "I do not have experience determining fault in cases like this. That is left up to lawyers, judges and juries." He was pissed!
My advice, thicken your skin. Your are in the big league now. Especially with multiple lawsuits.