I'll try to answer your questions in order:
Q: My question regarding this is: Once these pilots inform ATC that they can fly their approach visually .... what changes?
A: The pilots are informing ATC that they have the runway in sight. At this point nothing has changed and the pilots are obligated to fly their previous clearence. They are attempting to talk the controller into a visual approach, which saves time. As long as the crew has the airport or the preceding traffic in sight, or both, they can be cleared for a visual approach if the controller so chooses.
Q: Does this mean that the pilots (if cleared for a visual approach), are automatically flying under VFR rules, and as such, must "see and be seen" because ATC is no longer following their flight, regarding radar coverage and traffic separation?
A: The aircraft doing a visual approach are still IFR. A visual approach is one made under IFR in VFR conditions. The requirement is for the crew to keep the airport or preceding traffic in sight. They are still in radar contact, but when following traffic, the crew retains the responsibility for keeping the proper seperation between airplanes. This includes seperation with regards to wake turbulence.
Q: Does this mean that the flight crew's IFR flight plan is automatically cancelled?
A: No. At controlled airports, the IFR flight plan in closed by ATC on arrival.
Q: If a flight crew is cleared for a visual, does this simply mean that the controller is relieved of some of his workload regarding that particular flight because he knows the pilots can see what's around them?
A: Yes, it does, for a couple reasons. First, the pilots are given the responsibility for their own seperation, so the controller can reduce the in-trail spacing. This allows a higher arrival rate to be maintained at the airport. Second, there are fairly stringent requirements placed upon an air traffic controller in regards to the vectors he gives an aircraft intercepting an instrument approach (in the U.S. that is... I think Canada is the same). For instance, he may not give the aircraft a greater than 30 degree intercept to the final and the aircraft must intercept the glide slope from below (on an ILS). In addtion, the controller must seperate aircraft with regards to wake turbulence as well. So, as you can see, a pilot given a visual approach can save a controller time and energy.
Hope this gets you started on an understanding!