How to organize classes and interfaces in files

In a game project there is a CS file with character interface and derived classes, all about different characters and their properties. I assume there should be other classes for other game stuff.
1) Is it correct that I create separate file for another game object type, for example Weapon?
2) Is it correct to also include related interfaces in this file?
3) What is the role of interfaces here rather than just using a common base class?
4) Can you name a short example why I need interfaces in games?

Looks like I didn't know enough about interfaces here.

1) Correct
2) Correct
3) Define the functionality that the inheriting classes should implement
4) The same as interfaces in other applications

you do not want to combine interfaces and implementation classes in the same file
user of your class only interested in the interface - so this is what he should be able to see
your class could resize in the different assembly that could be delivered as dll without opening the code of the class
In this case just by adding dll with class implementing new type of character - you can extend the functionality of the application without rewriting the application code since it was only interested in the interface