You do not need to rely on your parents to provide original family documents for your future green card application. U.S. immigration requires an official copy of your birth certificate issued by a civil authority, which you can request directly from the government that issued it.

Addressing your specific document worries

You asked if you must obtain original vital documents directly from your parents or family of origin. You do not. The rules state that it is your responsibility to obtain and submit copies of records directly from the government agencies that hold them.

You also asked if official government copies or secondary evidence can substitute for original birth documents when the originals are unavailable. Yes. In fact, a birth certificate issued by a civil authority is considered the primary evidence of your birth. You do not need the physical original your parents hold; a newly issued official government copy works.

If a government-issued birth certificate is completely unavailable from the civil authority, secondary evidence is accepted. This can include early school records, baptismal certificates, or affidavits sworn by people who were living at the time and have personal knowledge of your birth. If you use affidavits, they do not have to be from your parents.

Finally, you asked what other documents besides your birth certificate you should make sure to get from your parents before cutting contact. For your own future Adjustment of Status (Form I-485), the regulations do not list any other documents you must obtain from your parents. The required items are things you hold or obtain yourself, such as your passport, Form I-94 arrival record, medical examination, and police clearances.