Qual è la differenza tra 殷切 e 心切 e 急切 ?Sentiti libero di rispondere con un esempio.

“殷切” means 深厚而迫切， it is a sort of emotion consist of “deeply concern” , “eager” and “high expectations”. Often used in describing the emotions teacher/parents to their students/children
Example: 我不能辜负父母对我的殷切期望。

”心切” means have a very strong motivation to do some things. But it is an adverb and can only be used after a particular behaviour to describe that sb is doing that eagerly，even blindly.
Example: 他们过河心切，根本不听。

“急切” is the emotion of doing something urgently. It is an adjective. Compare with “殷切”, it doesn’t contain the emotion of “concern” or “care”.
Example: 他急切地想知道问题的答案。