You can sponsor your sister, but it will take many years. Once your mother obtains permanent residence, she can sponsor your sister if your sister is unmarried. The issue of your other nieces and nephews is more complex, and the legal custody arrangement you have described does not make them eligible for any immigration benefits. You should schedule a consultation with an immigration attorney to chart the best course of action for your family.
Just as a US citizen can file for a parent, they can file for a sibling. There is no requirement for the parent to be in the US to file for a sibling. All minor children and spouses will immigrate with the sibling.
The above is intended only as general information, and does not constitute legal advice. You must speak with an attorney to discuss your individual case.
Yes, U.S. citizens can bring their adult brothers and sisters to the United States, but there is a very long waiting period of more than 10 years. Your mom may be able to bring your sister here more quickly once she receives her green card. You can check the Visa bulletin linked below to see the waiting times for all the family-sponsored categories.
Your sister would only be able to bring her foreign-born children (and only if she legally adopted them) to the United States after she gets her green card. By that time they would likely be adults and it would take even longer to bring them here.
www.gassonlaw.com - Disclaimer: This a general answer to your legal question. Unless you have a signed engagement letter with me, you should not consider this information to be legal advice.