1. Dear Makiko, there will be no need to prove your husband's previous five years bank statements and tax returns again. As you have had permanent residency for the last year, you have a free standing right, independent of your husband, to obtain citizenship in your own right. So, you merely need to show you have been visa free for one year by producing your Permanent Residence card.
2. The same applies to your son. He also has a free standing right, independent of your husband to obtain Uk citizenship based on his Permanent Residence in the UK for five years with one year with a Residency Permit. So, he can also make the necessary application for Uk citizenship.
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4. Dear Makiko, you will also need to show you had "comprehensive sickness insurance" as you were exercising EU Treaty Rights. This is basically a policy of health insurance which will have covered you for the last five years. Essentially, you need to show you were not a burden on the NHS whilst you were exercising EU Treaty Rights.
5. Dear Makiko, if you were working you would automatically have paid National Insurance contributions which would have entitled you to access the NHS and would constitute comprehensive sickness insurance. However, if you were not working, you need to show you had health cover. Even if you were working part-time, you would have paid NI and this would be sufficient.