itch.io

Hey. Sorry for the late reply! I am not sure if you can win the cooking contest early on. Mine was low so I lost anyway. As far as I know, the God of Love quest is just an extra quest. I have not needed it to complete other stories. I think he just gives you bonuses to your relationships. 

 a lot of if was trial and error or dumb luck xD

If I remember correctly, you have to finish the Priest's Angel Statue Quest. You get that quest after you complete Undercover Mission II with the police officers.