Everybody at the school, including the teachers and students, is happy when summer holiday starts.
Is this sentence grammatical?
Yes, it is. If you are asking about its 'punctuation', it is punctuated correctly. 'Everybody is happy' is grammatically correct. You can also use 'all the people ..... are' instead of 'everybody......is' here to sound more natural.
Hello, Emad—I agree with Ahmed that the sentence is grammatical. Regarding punctuation, "including the teachers and students" clarifies parenthetically that the scope of the subject of the sentence ("Everybody at the school").
Because the phrase "including the teachers and students" is parenthetical, it is set off by a comma at both ends. The sentence could alternatively have been written like this. Here the parenthetical element is an entire sentence:
- Everybody at the school (that includes the teachers and the students) is happy when the summer holiday starts.