Student information system
Yes, you can add more functionality to your project. You can take this in many different directirons such as adding courses that students and register for. 

As for a error handling, you could add a check in your set functions of the Student class to check for formatting or content and return a boolean value based on if they pass the validation or not. For example, since studentnum is a string, you can check to make sure that the format of letters and numbers if correct, if there is a certain format.

You could also use a try-catch block around the code where you read in the values from the user. Or validate that the user enter an acceptable value for each entry such as checking that when the user is asked to enter the age, check to make sure that they did indeed enter a number.