You are still washing out the other parts that are not gum tough.

Yes, the calories from gum stay in your body for 7 years

If I choose not to poo, do I eventually absorb it into food?

When you chew the extractable sugars get out and you swallow them. If you do not swallow and spit out even then part of it gets absorbed through the skin.

if it has calories at all then yea, the sugar or whatever dissolves into the saliva and you swallow that

if you can taste the sweetness then the calories are getting into your spit, so yeah--unless it's artificially sweetened.

Only like Tic Tac maybe I could Imagine. (Tic Tac mit der Frische der Kamaniolaminze und 2 calorien)

If it's a zero sugar gum, then no