When do I have to use 做/当 instead of 是?
In my opinion, 是 expresses a state 一种状态 and it's used to state a fact，while 做/当 denotes an act 一种动作, meaning 充当，担任.  For example, 我是老师 clarified the fact you are a teacher, while 我做/当老师 denotes you want to act as a teacher even if sometimes it's not really your job.