1. Generally speaking, if you are a resident alien (green card or substantial presence test) then you owe US income tax on all your world-wide income. You would report this business income on schedule C like any other self-employment income. It does not matter that your clients did not issue US tax forms like a 1099-NEC.
If you do not pass the substantial presence test for 2021, and you think you are a non-resident alien prior to September 2021, that would make you a dual-status alien for 2021, which is more complicated, and possibly beyond the scope of this forum to help.
2. As mentioned, this is considered US-source income under US tax law, because you live and work in the US, even if the clients are overseas. But even if it was not US-source, the fact that you are a resident alien means you pay US income tax on all your world-wide income regardless of the source.
3. If the country where this income was paid to you considers it their income also, you may be able to claim a credit on your US tax return for the foreign taxes you pay on the same income. But it sounds like this will not be an issue for you.
4. If you own a foreign bank account with more than $10,000 at any time, you must file an FBAR report. This is not included in Turbotax, the deadline is the same (April 15, 2022).
5. Do you need help on the general rules for paying taxes as a self-employed person? Briefly, you file a schedule C that reports your gross business income and deducts your business expenses. The net profit flows to your regular tax return form 1040 where it is combined with all your other income, deductions and credits, to calculate your overall income tax. You will also pay 15% self-employment tax on the net profit (this is the self-employed version of social security and medicare tax on your paycheck from a regular job). There's a lot more help available on the general question of how to file self-employment income. Here are some links.
https://ttlc.intuit.com/community/self-employed/help/how-do-i-report-income-from-self-employment/00/...
https://www.irs.gov/businesses/small-businesses-self-employed/self-employed-individuals-tax-center
