You can start the petitioning process from abroad. If your husband needs an affidavit of support, though, by the end of the petitioning process you will need to be domiciled or prove that you will be domiciled in the U.S. when he is ready to immigrate.
Whether your child automatically acquired U.S. citizenship at birth or needs to be petitioned along with your husband requires a more detailed analysis.
Very specific requirements have to be met before a U.S. citizen can lose her citizenship. This too requires a more detailed analysis.
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You cannot lose your citizenship if you've been gone for more than one year. You can file an I-130 visa petition for your husband and he can process through the consulate. If you can, register the birth of your child abroad and obtain a passport from the U.S. consulate.
Yes, you can petition for your husband from abroad. You also need to register the birth of your child with the nearest U.S. Consulate.
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