Your mother and your brothers will have to qualify for refugee/asylee status on their own.
Mr. Shusterman is a former INS Trial Attorney (1976-82) with over 35 years of immigration experience. His 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.
Only spouse or minor children can be derivative asylees. If your mom or siblings were to apply for asylum, their case is stronger, because you were already granted. They would need to show they have reason to fear as well, and the government will get your file to compare and look for inconsistencies or something that might indicate their case or yours wasn't true.
This reply is intended only as general information and does not constitute legal advice in any particular case. This reply does not create an attorney/client relationship.
No, but when you become a U.S. Citizen you can petition for your mother and brother. Mom will come within a year but it will take a very long time for your brother. You will be eligible for U.S. Citzienship after you have had your greencard for 4 years. You can apply for a green card after you have had your asylum status for 1 year.
Seattle Asylum Attorney
Legal disclaimer: This answer is offered for informational purposes only. It is not offered as, and does not constitute, legal advice. Do not rely on this advice without speaking to an immigration attorney in detail about your case. This message does not create an attorney-client relationship.