1) Please, do anyone know if they can have refuse a new application for EEA4 if I don't have the health insurance to cover the period my husband was a student?
Yes, they must refuse any application if eea national was a student and did not have health insurance. There is no way round it, no shortcuts.
2) could someone tell me if it is possible to apply for British Nationality without having a EEA4 I mean a PR card? ( I think my solicitor just took my money and lie to me all the time?)
It is possible to apply for British citizenship without PR card, but that is not the issue. The issue is, if someone is a student and does not have health insurance, then PR will not be granted and naturalisation will not be granted either.
3) how many months I have to make an appeal for EEA4 ? Because I have lost 4months on the British Nationality side now.
You cannot appeal now. Even when you had time to appeal, it would have been plain stupidity to appeal, as you would have lost the appeal one hundred percent.
I can assure you that your solicitor is either an idiot or he is on drugs or both. If a PR application fails, then naturalisation was bound to fail hundred percent. You solicitor deserves a shoe on his face.
regards