Someone is unfit if they are in poor physical condition, and get tired very easily when they do physical activity. The man in the photo is very unfit.
Unfit also means something that doesn't suit a purpose, for example a rotten fruit is unfit to eat.
When you vomit, some of the contents of your stomach comes out through your mouth. Vomit has a lot of acid in it and tastes very bad.
Babies vomit a lot when they are young, but they generally grow out of it.