Yes and Yes. But I'm a software developer... you probably want to chat with one of the people on our sales team. You're always welcome to call us for more details.
Technically speaking:
Yes, groups can do that.
If you use On Demand, you won't have to do anything special to give your outsourced users access.
If you're hosting FogBugz yourself, youl could do it by exposing (at least part) of fogbugz to the public internet. If you do that, I'd recommend turning on the 'Fog Creek Password Policy' once you install (make sure that no goofy passwords compromise your data.
A more secure method would be to give your oursourced users access to FogBugz via a VPN, thus keeping your FogBugz install off of the public internet. That's what we do here ;-)