Is it a good idea to cover the machine?
Covering it will prevent it from being coated in dust and grime but since it's inside (I assume), it offers little protection from anything else.
Can covering it cause problems (i.e. trap moisture)
If it were sealed and covered in a plastic tarp, perhaps moisture could build up, but if you cover it with a fabric cover and there is no moisture, you shouldn't have any problems. If your shop floods then you'd definitely want to make sure the machine was dry and the room well ventilated.
How can I protected against rust?
Best way is to prevent moisture from building up. Without moisture there will be no rust. But there are anti-rust formations you can apply or even paste wax is often used on cast iron surfaces to prevent rust.
Does the motor need to be run? If so, how long and how often?
Shouldn't be necessary since it's electric. The only reason I can think to periodic run it would be to ensure it still works and you don't find that it's dead when you urgently need it.