“Please ask him if he wants to move in, otherwise we will make our plans based on 3 people.”
But this is simpler:
“Please ask him if he wants to move in, otherwise we will plan on 3 people.”
“People” is already plural.
“Cheating occurred during the exam.”
This is OK, but it’s a passive voice. These would be better:
“Someone cheated during the exam.”
“Some people cheated during the exam.”