Thanks for your question. I will try to help.
Unfortunately, you now have to apply for permanent residence and received your permanent residence card before you can apply for naturalisation. If you do not have PR card when you apply to naturalise then your application would be rejected.
Although the restrictions no Romanian nationals have now been relaxed, you still have to show that you complied with the rules in place at the time otherwise the time may not count towards PR.
However, if you were self-employed and not studying between 1st January 2014 then it would probably be okay that you may not have had a yellow card and you would be now able to apply for PR provided you can show you exercised treaty rights for 5 years.
Once you have obtained PR you can wait a further 12 months and then apply to naturalise provi9ded that you meet the criteria on the following page
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If you were working self employed from when you came to the UK to January 2014 then it does not matter that you did not have a yellow card and then the rules were relaxed after that, so this means that you should not be rejected for this reason for PR.
Once you have PR you must wait 12 months and then apply for naturalization, yes.
If you do not obtain PR then what you have to do will depend on the specific reasons for the rejection.
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Yes, you can apply for your son as well. However, if you obtain PR then you can simply register your child as a UK citizen by applying for registration on his behalf. This is because he was born in the UK and because you have subsequently obtained PR whilst he is a minor, so I would do this instead.
The webpage on applying for registration for your child once you have PR is here:https://www.gov.uk/government/publications/application-to-register-child-under-18-as-british-citizen-form-mn1
If he has been here on his residence card then he should apply for PR at the same time as you, yes.
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Thanks. you too.