Does God answer the prayers of a sinner?

They aren't.

When you pray, just believe that what you want, Jesus will give to you in due time if it is His will. Talk to Him like you would an earthly friend, and your answers will be coming much sooner than you may be used to. Jesus will always answer you, somehow. Like His parable about the corrupt judge and the old widow. Your Father in Heaven loves you more than anything, and if that mean old judge was willing to give that poor widow mercy, surely God would do the same for you, much quicker than how long it took the stingy judge to answer the widow. Have faith my friend, and hope to see you in heaven!