Questions about health insurance and national pension for D-10 visa holders

It's been a few months since I received my D-10 visa, and I'm a bit confused about health insurance and national pension matters. I'm seeking advice from those who have experience with this. First, regarding health insurance. I read online that if you have no income while on a D-10 visa, you can receive a discount on your insurance premiums. So, I called the English consultation center, and the consultant said it's not possible and that I have to pay the full amount. Has anyone else had experience receiving a discount? Or have the regulations changed recently? Now, about the national pension. I received a notice to pay into the national pension. When I contacted the pension office, they told me that since I currently have no job, I don't need to pay, and that my employer will handle it once I get a job. However, I think I read about cases where issues arose due to unpaid pension contributions when extending a D-10 visa. Given that I'm currently unemployed, is it okay to ignore the national pension, or should I insist on making contributions? I would appreciate any help. 😭😭😭