Hey Raffles -- happy to help with these questions. I'll go number by number.
1. When they ask, I think it's ok if you describe that to them to see what they think. They may also want to add that to your records with them and check in later with you about it. Typically, periods occur every 21 to 35 days, the average being 28 days. It sounds like you're right in that range, so they will likely tell you it's normal.
2. Generally when a doctor asks if you are sexually active they are assessing if you are at risk for pregnancy and/or of sexually transmitted infections. Solo masturbation does not have these risks, so you - in their eyes - are not sexually active. You answered correctly!
3. To my knowledge, not being sexually active is not a barrier to getting an IUD. They may talk to you about other contraceptive options just for good measure. I'm not entirely sure what their protocol is, but they might ask why you want one if you are not sexually active and explicitly do not plan to be. Not to challenge you maliciously, but because you are not at risk for pregnancy. Would you feel comfortable talking with them about that? Do you have any questions about IUDs that we can help answer?
Also, have you ever taken a look at our resource Your First Gynecologist Visit
? I know this isn't your first time, but because this is still a relatively new experience it might feel good to read through it. I know I get a little nervous when I'm at the doctor sometimes!