Could bad grounding cause sparks and fire when connecting the cable box and TV?
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.