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.
In a perfect world, with perfect electronics, there would be no need for a grounding conductor. It's there to deal with imperfections. The most likely case for a ground fault in this installation would be if the black conductor lost some insulation and shorted itself against the frame of the fan. In such a situation, the casing could become electrified, and a grounded person, touching the fan body could receive a shock.
If it were properly grounded, you'd get a short circuit to the ground wire, and the breaker would trip.
However, the fan is mounted to the ceiling, and the possibility of someone touching it is low. (Unlike, for example, the frame of a fridge or stove, where human contact is part of normal operation.)
So, Is it safe? Quite likely. For added safety, turn the wall switch off when changing bulbs. Is it to code? No. -- Unless, as others have suggested in comments, the mounting box is grounded on the other side.
You can however, locate the breaker, and replace it with a Ground Fault Interrupt breaker, which would trip should a ground fault occur. This isn't something you should do yourself unless you have experience working in the panel.
Another possibility, if your switch happens to be chained off of an outlet, which is quite possible, depending on the routing of the wiring on that circuit, is to replace the outlet with a GFCI outlet, and wire the switch to the load side of it.
Best Answer
Yes, typically ground wires can be extended. It's always best to replace the entire ground wire, from the connection point, instead of splicing it when possible. I'm not sure if the ground wire you are speaking of is in a flexible pipe, part of a cord or an external green wire. That information (possibly a picture) would make it much easier to answer your question thoroughly.