You said it right, of course God still answers prayers, just like you said most people only prays with different intensions while the actual intension they should be praying is left out, and another thing that seems as if God is not hearing and answering our prayers is sin, God is a merciful God, he is always ready and eager to answer our prayers but soon is a reproach, only if we can accept our sins and confess them to God his always ready to accept and forgive us,