Hi andy2016losangeles! Congratulations on your growing family...how exciting.
To be claimed as a dependent, a person must be a citizen or resident of the US, Canada, or Mexico. Also, they need to have a social security number.
Your new daughter will probably be the first eligible to be a dependent since once you register her as a US Citizen you can apply for a SSN for her. After you have the SSN, you can claim her for Child Tax Credit.
Your wife and two other children may not be able to qualify as dependents until further into the immigration process. They would need to have SSNs and either be a US citizen or resident. While they are living in El Salvador and are not citizens of the US, Canada or Mexico they are not eligible to be a dependent.
Also, I should mention that there is no adoption credit available for adopting your spouse's children. Unfortunately, this is a rule in US tax law. https://www.irs.gov/taxtopics/tc607
"Qualified adoption expenses don't include expenses that a taxpayer pays to adopt the child of the taxpayer's spouse."
To change your status with payroll, simply complete a new W4 with your employer. However, be aware that until your spouse has a SSN, you cannot file a joint return with her, so you might want to hold off on doing this until further into the immigration process. Otherwise, you could be withholding as married/jointly but may have to file as married/separate and will end up owing taxes. It is safer for now, and would be my recommendation, to continue withholding as single.
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