What are my chances for getting into top universities? (asylee student)

The two schools I mentioned are Cooper Union in NYC and Berea College in KY.

Cooper Union offers 1/2 tuition scholarships to all applicants plus would likely cover much more in your situation.

Berea is free; students work on campus in return. For example, many maintenance and housekeeping functions are handled by students.

Good luck and keep us posted!