Do I need to file U.S. taxes if I obtain a Schedule K-1 form from my regional center?

This question may be better addressed by a CPA or a tax attorney, but my understanding is that until you have obtained lawful permanent resident status and/or also depending on how many days you have been in the U.S. you may not be subject to U.S. tax.

Check with an international tax person. It may depend on how many days you have spent in the U.S. You have to pay taxes on your worldwide income once your conditional residence is approved but should check any tax treaties between your country and ours.

You should contact a U.S. accountant who understands your situation.

No, you do not have to file any tax returns.

For single dependents who are under the age of 65, you generally must file a federal income tax return if your unearned income (such as from ordinary dividends or taxable interest) was more than $1,050 or if your earned income (such as from wages or salary) was more than $12,000.

It depends on the amount you earn in the USA. Ask an accountant.