EE3 form and insurance for student whilst living with parent

Hello everyone!

I'm just really confused at the moment, I've been living in the UK since Jan 2008 and at the time I was 15. I moved with my mother and brother (16 at the time) in which we went to the local school and my mom was in the employment. All of us are EEA nationals.

When my brother turned 19, he started full time employment, also my mom never was out of job.

This year I'll be 22 and I'm doing a degree at university (will start my last year in September), I'm wholly dependent on my moms and brothers wages on top of that I take out the maintenance loan from uni and last year I've been also given a grant.
The thing is hence I'm a student I never had a insurance taken out, I just never thought about it, we've got EHIC cards however they were issued by the UK and mine expired ages ago. I've also worked but it was never more than 6 months (both part time and full time) in a year since I've turned 18 will that somehow negate the need of the insurance? Also I've been thinking about getting insurance now, surely that will somehow be beneficial i.e. showing that I don't want to be a burden on the state since I'm not really a child anymore.

The main reason for the application is that I want to gain UK citizenship eventually however I feel that sending application on my own will not succeed due to the insurance issue. We are planning to send our application together and kind of explain that I was a child (I think its anything under 21 years of age) during the qualifying period hence I didn't needed an insurance? Correct me if I'm wrong please.

Would my application be rejected on the terms of lack of the insurance, I mean logically its not as if I could have one at the age of 15 and my mother didn't needed one as a worker, will I be exempt from that requirement due to that?

You probably attained PR as a family member of your mother, after she exercised treaty rights (eg worked) in the UK for at least 5 years.