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If an array is defined inside of a method, it can be passed as an arg to another method that is called from that method:

void aMethod() {
int[] anArray = {1}; // define an array in this...

Sorry I don't understand your question.
An array can hold many values.

What do you want the method to do?

The code still has the recursive call. That should be removed and a loop used instead.

That is probably because of the recursive call:

studentNumberEntered(number, sc);

Use a loop instead of a recursive call.

Put the code in a while() loop that continues looping UNTIL the user enters the desired input.

Put the code that causes the exception inside a try{}catch block. The catch block code will get control if an exception is thrown.

I don't know any way to stop a user from entering whatever he wants. The program can refuse to accept what is entered and ask the user to enter what the program wants. This can be done repeatedly...