Perhaps. The rights would be for the basic "proof of concept" device. If a lot of engineering work needs to be done to make it a viable product, but they think they CAN make a viable product, then the researchers can create a corporation to do that, license the basic technology, patent the incremental technology needed to make it a real product, and make money.
Not if it had anything to do with what the person was working on. If it is something completely apart from job duties then you can do as you suggest
Case law is very clear on this