What do you call the red hangings on her hat?

Since no one else seems inclined to answer you--it's called a tassel.

Thanks.
BTW, how to describe (in native English) the process in which the senior scholar removes the tassels from the (doctoral) hat which represents the complete of the graduation ceremony?

It is not removed. It is moved from the left side of the hat to the right side to show that he/she has graduated.

In the U.S. at least, the tassel is not removed.

However at the end the the ceremony, all the students, on a given cue, all move their tassels from the right side of the motarboard (the hat they wear) to the left. This signifies they are now a graduate, and not a student. The teachers who are already wearing motarboard are wearing their tassels to the left throughout the ceremony.