You can file as married-joint, as long as you entered your spouse's income on your return, or if she didn't have any income. I am assuming she has a social security number, which is what I understood.
Since the children are US citizens by birth, you can claim them as dependents if you have a social security number for them, provided they qualify as dependents otherwise. You can enter them in TurboTax and answer the questions to see if they qualify as dependents. You may qualify for the credits associated with dependent children if they qualify as your dependents.
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