it is like rinsing the mouth.

As for vomiting, deliberately inducing it invalidates the fast, whereas being overcome by vomiting does not.

Applying oil undoubtedly does not invalidate the fast. Unavoidable bleeding—such as non-menstrual vaginal bleeding, bleeding from wounds, nosebleeds, and the like—does not invalidate the fast. Menstrual and postpartum bleeding, however, invalidate the fast by scholarly consensus.

As for cupping, there are two well-known opinions. The position of Ahmad and many of the early scholars is that it invalidates the fast. There are two opinions within his school concerning bloodletting and similar procedures; one treats them as equivalent to cupping. His position regarding kohl that reaches the brain is that it invalidates the fast, like perfume, and when needed (1). Mālik holds a similar view. As for Abū Hanīfa and al-Shāfiʿī—may Allah have mercy on them both—they do not consider these things to invalidate the fast. Allah knows best.