the feeling of dizziness and fear, and of losing your balance, that is caused in some people when they look down from a very high place

that 引导定语从句，修护the feeling。前面虽有逗号，但不是非限制性的。在 balance 之后的逗号，是因为and 前有逗号，为了对称而作的停顿。用that 或which 都没错。

the feeling of dizziness and fear, and of losing your balance, that is caused in some people when they look down from a very high place ——

整个是一个名词性词组。of dizziness and fear, and of losing your balance 是the feeling 的定语，that...place 是定语从句，when...place 是定语从句中的时间从句。