How are the nose or teeth cleansed of blood if it comes out of them? Is this done by frequent rinsing and sniffing water into the nose?

Purifying the teeth or nose from blood is achieved by removing its color and odor with pure water. It is sufficient to have a strong presumption that the blood has been removed, not absolute certainty. If the bleeding is profuse and difficult to stop, it is excused due to the hardship.