Can this also mean "they are in the school"?
Yaa :)
Is ada necessary here?
No.
"They are at the school" should also be accepted.
It sounds a tiny bit unnatural in english, but I guess it's correct
It seems logical for it to translate to "they are in the school" as well. Is this correct too?
They are in school
at school sounds about right to me. perhaps AE/BE issue?
Mm