Is this a correct usage?
How do you spend a typical day at school?
What are the alternatives?
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Your example sentence How do you spend a typical day at school? is perfectly correct. In particular, the idiom to spend a day is correct. Furthermore, you are allowed to modify the word day with an adjective or other modifier without harming the sense of the idiom (which isn't true for all idiomatic constructions). So your use of a typical day is completely correct and expresses what you are trying to ask very well.
If you're using "how", then it is "how do you [insert verb]". Eg. "How do you spend a typical day at school?" is correct.
If you're using "what", then it is "what is". Eg. "What is a typical day at school for you?"