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Good question. Yes, Aleksandra and Mona are both right. Eg. '... and after that he/she could not be there...' is better written '... and after that they could not be there...' (in my opinion). 'He/she' is very clumsy.

Yes, you can use the form "they" when you are not sure about the gender.

Do you mean in a sentence like eg. "A student should choose a subject he/she enjoys"? Then you can use he/she or 'A student should choose a subject they enjoy". Both forms are correct.