Hi Leonel,
You have asked several questions. I will try to respond to them as best I can.
Child support does not automatically make you the individual that can claim the child as a dependent. Does you divorce agreement stipulate you as the one claiming the child. If the agreement is silent or if there is no agreement, the parent providing more than 50% the support is the parent entitled to take the dependent.
The newborn is would depend on you providing the support of the child.
Your dad the rules are somewhat different. In addition to providing more that half support of your dad, he has an income limit of $4,400.
You do not need a US residence to be required to file a tax return. If you are a US citizen or have a green card, you need to file a form 1040 on your worldwide income. You may qualify for foreign income exclusion or foreign tax credit. I am attaching an article to help you on that. There is also a credit for taxes paid on foreign income. I will attach an article on that.
Here is an article to assist you on the who is a dependent.
https://turbotax.intuit.com/tax-tips/family/rules-for-claiming-a-dependent-on-your-tax-return/L8LODb...
Here is an article to assist on foreign income exclusion:
https://www.irs.gov/individuals/international-taxpayers/foreign-earned-income-exclusion#:~:text=Howe...
Here is an article on foreign taxes paid:
https://www.irs.gov/individuals/international-taxpayers/foreign-earned-income-exclusion#:~:text=Howe...
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