Do you pay taxes for whole year on your first year in US? How to claim discount on health insurance?


Good day all, if we first entered US on September 2022 and became lawful residents, should we declare the income earned in prior months for this year?
Also do you know if scholarships from universities are taxable and if receiving health insurance credits can influence our status in some way?
One more thing, if we plan to pay taxes in our country for current year, should we pay them again in US if there is a tax treaty?

Regarding health insurance credits, since Medicaid is not available to immigrants, am I right that even low income below FPL like 20 000 per year will make me available for tax credit and out-of-pocket cap limit (2800$ for single person)?
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