It is not the quality or beauty of your singing that quietens (well, spelling check here says that should be "quiets" the child, I don't know) anyway, back to the subject at hand..........the baby helps him to relax and go to sleep....it's the hum of your voice. As long as you're not bothering any one else, Sing up a storm!!
A warm bath and a rocker works great each baby is diffrent so try things and see what works best for yours babies could care less if you are a singer it is your voice that soothes and makes him feel safe and secure
A baby will adapt to how each person puts them to sleep. You're going to have to let them cry to learn. My husband just sets the baby in the crib and shuts the door. My nanny gives him the bottle while rocking him and then lays him down and rubs his back. FYI i am handi capped so i cannot carry the baby