Do I have this status after I enter the United States?
Yes, but you need to apply for asylum generally within one year of arriving in the United States.
Is this a status that can lead to citizenship?
Yes, if your asylum is approved, then being an asylee can lead to citizenship.
Is this a status I can get based on being a victim of violence?
Sometimes
How do I qualify for this status?
You must show you are afraid to return to your home country because you have been harmed or could be harmed if you go back, you must generally file an application for this within 1 year of coming to the United States. If your application is approved your status changes to asylee
Can I get a permit to work, government ID, and/or SSN?
Yes
Is this a path to getting a Green Card?
No
Can my family member get immigration status through my status?
Yes, spouse and children