Can I apply if I am convicted of a crime? Yes, you can but it will depend on what kind of crime it was.
Who will determine if I will be granted asylum? Immigration officer or a judge of the immigration court.
How will it be determine if I am granted asylum? You will have to meet the definition of a Refugee.
How is a Refugee determine? This will be based on the information you provide on your application. Also the information you give at your interview or hearing.
The interview or hearing is very important so make sure you have your facts correct and in order. The interview will last at least an hour or more and will be very intense so be prepared.