Sounds like Another Door - Isekai Kaikitan.
It's about a girl and her father who traveled to places via a magical door.
Yes, the girl and her father were on a journey to learn more about human behaviour. They approached humans in trouble, and offered them the "Door" which would lead them to the world they wanted or their ideal world where their troubles would be resolved. What lied beyond the door was different for each person.
1) One of the stories is about a girl who didn't like vegetables and went to a world without vegetables through the magic door.
2) Another story is about a girl who was not satisfied with her appearance and obtained a knife which can change her face and body. However, she overused it and her face became scary.
Yes, I remember this two stories were indeed in the manga, since I've read the manga multiple times (one of my relatives had a copy). I also cross-checked with my sibling, and she remembered it too. Below is the more detailed version of the two stories you remembered:
1) What lied beyond the door was a world without vegetables where people only ate sweets. Eventually, her body weakened, because people from 'this' world needed more than sweets to keep their health. In the end, she realized how important vegetables were for her body, and she went back to 'this' world.
2) What lied behind the door was an operation room to make her beautiful. The girl stole the knife and operated herself, thus didn't need to open the door anymore. As she became more and more beautiful, she entered the entertainment world. In the end, in a photo shoot (I forgot the exact context, but her image would be taken with camera), when she tried to smile, her mouth tore in both side, making her look like Kuchisake Onna/Slit-Mouthed Woman.
According to the link I gave above, no chapter was ever scanlated.
