I was checked out by my doctor and she said I have an anal fissure. My question is, do anal fissures bleed a lot? And do they cause blood clots?

Depends. There are a lot of qualitative terms in your question. Anal fissures normall cause bleeding that you see on the toilet paper or toilet bowl. A small drop of blood in a large bowl of water can seem like a lot of blood. Depends on how you are rating what a lot of blood is, when and where you are seeing it and other symptoms. Blood clots are not typical for a fissure, but possible.