Do we need to support multiple operations before the "=" button is pressed? So would we need to support something like 1+2+3= ?

No, feel free to support just one operation followed by an "=". It's not hard to support more (but it's not required).

Do we need to support unary minus ?

No

What if the result of an operation overflows? Do we need to do something special to catch this, or can we just assume that the user doesn't do any operations that would result in overflow?

You don't need to worry about overflow, just display whatever the result is (even if there was an overflow and the result of the operation is not correct).

Does our calculator need to look pretty?

No part of the grade will be based on how pretty your user interface is, just make sure that it is usable...