For the most part, the words are interchangeable. Distinguishing between multiple examples of such things can be aided by their individual connotations:
a line on the surface of something along which it has split without breaking into separate parts
A crack tends to be a visible flaw that can splinter or spider into larger cracks with many smaller, attached cracks. The defining point of a crack is that the cracked object is still together — no matter how tenuous. Often there will not be any visible negative space or hole. Most cracks can be felt by rubbing your finger or hand over it.
a long, narrow cut or opening
The biggest difference between a slit and a crack is that a slit implies some form of opening. Cracks also tend to be on a surface; a slit can be in virtually anything. A stereotypical slit is one that causes some portion of the object to pull apart — large slits can go all the way through to reveal a clean hole.
a narrow opening or fissure, esp. in a rock or wall
A crevice is typically reserved for very large objects that have been separated into more than one distinct section. A crevice in the earth would be something that separates two plains; a crevice in a wall could very well separate the wall into two pieces. "Narrow" is respective to the larger object. A crevice could be meters wide or only inches. A typical crevice is also very deep.
a tear, crack, or fissure in something, esp. down the middle or along the grain
A split more directly conveys an object being split into smaller pieces or a longer top-to-bottom crack. A split could also be used to describe pieces that are no longer attached at all. There is no implication of depth with a split; the importance is the length of the split or how much of the surface remains unaffected.
a fissure or split, esp. one in rock or the ground
When I think of a cleft I typically envision a V-shaped hole. A "cleft in the rock" is a V cut sideways into a mountain that can provide shelter. The "cleft of the chin" is the middle gap in some people's chins. Depth is important to a cleft but the gap will not go all the way through.
To directly address your example of a flaw in the bottom of a bowl, I would expect crack to be the most applicable. If there is a chunk missing but no thin lines it could be best described by chip:
a small piece of something removed in the course of chopping, cutting, or breaking something, esp. a hard material such as wood or stone