The LPR can file for her unmarried son. He will change from F2A to F2B automatically when he turns 21. The LPR can also apply for naturalization when eligible, which will probably speed up the process. However, it will still take at least several years from now for a visa to be available (for the priority date to be current) before her son can adjust status in the U.S. if he is maintaining nonimmigrant visa status.
A U.S. citizen sibling can sponsor a sibling. This is the F4 category and generally takes the longest. The two immigration petitions will not conflict with each other, so there is no harm in filing.
Yes, she can sponsor her son for a green card. Please see
Mr. Shusterman's 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.