This is a fairly "common" issue, that typically occurs due to high resistance at the terminal. The high resistance can be caused by corrosion, or a loose connection. The high resistance causes heating, which causes higher resistance, which leads to more heating. Eventually the insulation on the wire starts to melt, and/or burn. Usually the heat will transfer through the terminal block, and into the smaller wiring in the stove. When the heat becomes too much, the smaller appliance wiring will fail and open the circuit.

In most cases this is not a super dangerous event, as the wiring is contained within the stove. However, there is a chance that this can lead to a fire in the house, especially if the cover is not properly installed.

Causes

Corrosion

Corrosion is more commonly a problem if the wiring is aluminium, though can still be a problem with copper wiring. Because stoves/cooktops/ranges draw large amounts of current, there is typically some heating of the wiring during operation. The constant heating and cooling cycles of the wiring can lead to corrosion, and/or hardening of the wiring over time. This corrosion and/or hardening increases the resistance of the wiring, which cause the heating to be worse.

Solution

Occasional inspection of the terminal block and wiring, can prevent the corrosion/hardening from getting too bad. If you notice any discoloration or corrosion, have the cord replaced. There are also conductive pastes available, that can be applied to the wiring and terminals to help prevent corrosion. While this should always be used with aluminium wiring, it may also be applied to copper wiring.

Loose Connections

This can be caused initially by not tightening the terminals to the proper torque (usually specified by the manufacturer), or over time by heating/cooling cycles. Loose or bad connections can cause arcing and/or higher resistance. As discussed before, high resistance leads to heat.

Solution

Make sure all terminals are tightened to the manufacturers specifications. It's also a good idea to tighten the terminals after a few hours of operation. As stated before, occasional inspection can also prevent this situation.

Why didn't the breaker trip?

The heating was localized to the stove\cooktop\range, so the thermal protection in the breaker would not trip. Since stoves\cooktops\ranges draw large amounts of current during normal operation, the current during the event likely didn't go high enough to cause heating in the breaker to trigger the thermal protection. It could also be that the breaker is faulty, so it should be inspected.

Is the stove scrap?

The stove may be salvageable, though you'll want to thoroughly inspect all the wiring to insure it is not damaged. Replace any damaged wiring with equivalent parts (cooking appliances use high heat resistant wiring).

If the stove is still under warranty, you'll want to contact the manufacturer to discuss your options.

This is a very suspicious situation.

Adding a proper ground to every receptacle in the house is no small feat, it's weird that the handyman just casually mentioned that he did it. I believe the only correct way to do it would be to run a new ground wire of the proper size back to the service panel where it can be connected to the grounding rods.

Perhaps the handy man just used pigtails to ground to the box, as @SpeedyPetey says. Or maybe he connected the ground to the neutral, which would be good enough to fool an outlet tester. Or maybe he accidentally connected the ground to the hot side, which might explain your sparks. (Many appliances have their metal housing connected to ground. If the exterior of one of your appliances was actually electrified that would explain the sparks.)

If you have a simple outlet tester you could start with that, but it will not detect all faulty conditions like a ground / neutral swap or connection. You could also shut the power off and pull one of the receptacles off the wall, to see if you can tell what kind of grounding, if any, is actually there.

I suspect you will want to get an electrician and your real estate agent involved.