If you give food to Clara she will get nutrition and the babies grow much larger. So I believe how you're suppose to be playing is having Clara eating what comes to be a breakfast, lunch, and dinner and the side effect is having too large of a belly. Very rough estimate, but it's 50 nutrition per belly size. Once Clara has a large pregnancy she will be encumbered. So consuming some higher tier food such as the watermelon tea or others will resist that and let you keep running instead of forcing you to walk.
You can just turn it off at Clara's dresser in her room and not worry about it which is my suggestion. Unfortunately there isn't enough variations in the game to force you to eat those foods or have an issue with it really. Just a neat little game.
I think you mean the circle symbol thing. If I recall correctly it has to do with a secret once you climb that ladder or get to climb the ladder. It also has to do with either the day of the week and/or the cave below.