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.
You would appear to have a high resistance section somewhere - when you say half a circuit, do you mean:
As to which side is high-resistance (hot or neutral) what voltage to you see when measuring from hot to ground and turning on a switch or plugging in an item? In the unswitched state it should be the same 118V (or so) as hot to neutral. If it remains at 118V (H-G) when you flip or plug and something goes dead, you have a high resistance on the neutral side. If it goes dead (H-G) the high resistance is on the hot side. In either case you don't have an open circuit, since you DO have voltage when nothing is on - you just have very little current available, because something is just barely connected, or a wire is mostly chewed through, or something like that.
To the extent that you can infer (or know) the layout of the circuit, the problem is between the last working item and the first non-working item. You can use various methods to track it down - turn off everything, turn off the breaker, use your multimeter to check resistance between hot and ground while running around with a low-resistance load like a heater or incandescent light and plugging it into various outlets (circuit breaker off, remember!) If the load reads as (say) 5 ohms (on its plug) you will see something very close to 5 ohms when plugged into outlets well-connected to the outlet you are reading at, and some much higher number when plugged into outlets across the problem area. Eventually you may be able to isolate to a particular cable, at which point you can pull the outlets, disconnect the cable, wire-nut black and white at one end and read resistance at the other end.
You may, ultimately, have to rip open some walls to follow the problem cable and find the problem. You should not have to "replace every wire in the circuit" or anything like that. If ripping the walls open is a big problem, you may be able to disconnect the bad cable section and run new wire up or down the wall without making new holes in the face of the wall to run a new cable in the basement or attic to bypass the bad cable.
But you may, by careful checking this way, find a bad connection you have somehow missed, rather than a bad cable. Be open to either possibility, and work to isolate where it must be, whichever one it is, from both the working and non-working parts of the circuit.
You may also want to try using your NOSE as much as you can - the flickering you report happening earlier was probably associated with some arcing - there is likely to be some burnt material at the location of the problem. If you smell burnt insulation anywhere, you're close, probably. If anything was nailed or screwed into the walls about the time the problem started, look there. Otherwise you may be hunting rodent damage, and that probably will take opening up the walls to find.
Best Answer
It sounds like they have a floating neutral in the power. If outside at the cable junction box take a look at the connectors. If they are burned or melted then it is a floating neutral and the power in the house looked for a ground which the cable lines are grounded with the house electric. This allowing the cable to get energized which can cause the fire