Do you push down singing?
Avoid intentionally pushing down the back of your tongue, as most people do when first trying to drop the larynx: If you push your tongue down, you also feel the larynx push down and you feel a tightening of the muscles under your chin. This tight sensation isn't what you want for singing.
Should you suck your stomach in while singing?
Your sternum/breastbone should be strong and erect with no sagging and focus should be placed on drawing the breath low into the body. Your stomach must never be sucked in during singing!