No this shouldn’t impact the form validity.

Yes you should update at the airport and through form AR11.

You may file the application and if denied, can reapply. Should not impact your permanent residency.

You may enter on a tourist visa and within your authorized stay period.

Possibly provided other secondary evidence of his birth and statements. Consult with an attorney for guidance.

Best to consult with an immigration lawyer from Finland.

Best to consult with an attorney to explore your options based on her background.

Yes the US should be your country of domicile.

No you do not need to refile the I130.

It is best to have an attorney assist you and review your entire case file.