File an I-130 for each family member. However, consult an immigration attorney for filing an I-130 for your sister, as this will interfere with her entry (or change of status) on a student or visitor and many other nonimmigrant categories.
The I-485 can and probably should be filed concurrently with the I-130 for each parent. An I-485 cannot be filed for your sister as there is no visa availability in the 4th family preference category for at least 10 to 13 years. Your sister cannot remain in the U.S. if her parents no longer have H1B/H4 status.
A parent can sponsor a child in the F2A category, but it will take time and your sister will probably have to depart the U.S. Consult with your current immigration attorney for case specific advice.
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Your parents can file I-485s simultaneously with the I-130s. However, your sister would face a 12-24 year wait for a green card through you. You should sit down with an immigration attorney to discuss your sister's situation prior to filing any paperwork. There may be better options (e.g., your father immigrating the family through his employment, for instance.) Please see
Mr. Shusterman's (former INS Trial Attorney, 1976-82) response to your question is general in nature, as not all the facts are known to him. You should retain an attorney experienced in immigration law to review all the facts in your case in order to receive advice specific to your case. Mr. Shusterman's statement above does not create an attorney/client relationship.
1 and 2. Only your parents are eligible to file for an I-485 each concurrently with your I-130 for each of them. Your sister is in the siblings category which can take up to a decade and a half to process and have an available immigrant visa number. The filing off and I-485 is not "mandatory "if parents do not intend to apply for adjustment of status immediately and opening green cards within six months or less. Totally optional.
4. Your sister will not have the right to remain in the United States merely because you file an I-130 petition on her behalf. She will need to maintain valid non-immigrant status throughout the years that it is pending, should she wish to remain in the states. Parents of a US citizen are deemed to be "immediate relatives" and as such will be able to apply for and obtain their green cards in the United States and obtain it within six months or less. They do not have to leave the US.
3. You have to submit one original affidavit of support for either one of your parents' I-485 package and attach a copy thereof in the second parent's I-485 package.
Kindly be advised that the answer above is only general in nature cannot be construed as legal advice, given that not enough facts are known. It is your responsibility to retain a lawyer to analyze the facts specific to your particular situation in order to give you specific advice. Specific answers will require cognizance of all pertinent facts about your case. Any answers offered on Avvo are of a general nature only, and are not meant to create an attorney-client relationship.
If you are a US citizen, you can file an I-130 (relative petition) for your parents. They can file an I-485 at the same time, along with the I-864. Look at the form directions on the USCIS website for forms to file with the I-485 and I-130. It will be important to make sure that your parents are admissible before filing any forms. The most common reasons for being inadmissible have to do with criminal convictions and immigration status issues. As my colleagues point out, although you can file an I-130 for your sister, she is not eligible to file an I-485 at the same time. She will have to wait until a visa becomes available. This can be a very long wait. In the meantime, that fact that you have filed an I-130 may impact her ability to enter the US on a temporary visa such as a student visa or visitor's visa. There may be better options for your sister. The issue should be explored with an immigration lawyer.