No, chalice doesn't work when starving. It augments the natural healing from being sated.

Yes, Ring of Haste and also Glyph of Swiftness cause you to be less hungry because it takes fewer turns to walk around.

I would not craft meat pies because then you're basically eating three pieces of food all at once instead of spacing them out. You risk being at full health and wasting the healing from them. It sucks to eat food when low on health, being nearly one-shotted by some attack, needing to use a healing potion, and then wasting the healing the food would have given.

The satiety from a meat pie is exactly equal to that from the component foods, except having the well fed buff makes you heal a little more than being sated normally does.

I've done On a Diet, and after a while you just don't worry about food and eat healing potions instead. The food becomes a nice bonus to stop the hunger pangs for a while. The Recycle spell is your friend here.

You can also craft Honeyed Healing and Aquatic Rejuvenation. The latter is really good. You heal +3 with every step in water, and the buff only runs down when it's healing you. It doesn't expire with time. With my meager testing, it's basically two health potions. I was nearly dead, slept in a puddle until full health, and still had half of the buff left.