I had a similar problem with GM headlamp switches, the older ones mounted on the dash. These, too, have a thermal breaker built into the switch, also has the dimmer potentiometer. These swithces were put together with crimp tabs and some of those tabs were part of the electrical circuit. After a few of years, the plastic parts shrink and the tabs in the electrical circuit loosen. (In my opinion, a bad design detail.) These heat and causes the breaker to trip. Headlamps may flicker too. On mine, it would trip out when on high beams, but was ok on low beams. As luck would have it, mine failed at dusk while I was on the way home. An oncomming police curiser saw my headlamps acting up and I was fiddling with the high-low beams. He turned around and chased me down - thought I was signaling him. LOL - I had some explaining to do. I made it home with the low beams. My solution was to replace the switch since I already had another one. However, I experimented and found that I could repair the unit by soldering the offending connectors, only the ones in the electrical circuit. I chose to continue with the new switch and keep the repaired one for a backup. One never knows if he messed up the thermal trip calibration while soldering. That shouldn't happen if the solder job was done quick enough without overheating the internal parts. By the way, did you find a problem in removing the switch from the dash? The knob and shaft won't pass through the hole, and the knob is permanently fastened to the shaft. There is a trick. The knob and shaft will come out of the switch. Somewhere in the switch housing is a small release button, usually on top. Press this down and the shaft will pull out.

Your electricians were in likely a "rush" and not talking to you because they are unprofessional and doing ILLEGAL work. Were there permits pulled and inspections done? From the magnitude of the work done, I would suspect that you really should have brought all the kitchen wiring up to code. Certainly no NEW receptacles in the kitchen should be on circuits in use elsewhere in the house. As you realized the ITE Pushmatic panel you have isn't the greatest. Having the mechanical part of the breaker fail such that it won't turn on or off is not uncommon. I'm really concerned that they did a lot of "rearranging" on this older panel. It makes me wonder just WHAT they were doing. As for things that won't come on, I'd look for GFCI's that are tripped. Note that a GFCI on a circuit can protect the other outlets. Only the countertop receptacles are required to be GFCI (unless your appliance manufacturer's information requires it for the appliance). The bare wiring you see is hopefully the grounds. Properly stowed in the box, it is fine. Nothing that's supposed to be carrying electricity should be in a position to touch the bare wiring. There should be a cover on the box. Frankly an electrician shouldn't have left it without a cover but often they do when other trades are buzzing around (painters or tilers). What outlet with no ground? A receptacle with a ground pin has to be grounded. If you have older ungrounded two pin receptacles that is probably OK. If it has the three prong then they should not have put that directly on the old ungrounded branch circuit. The only way around this is to have a GFCI there (and even then it should blatantly say NO EQUIPMENT GROUND). This isn't something we are going to diagnose too well via forum posts. You should have an electrician (either the clowns you were using before or a new one) come and answer those questions.

Get a different electrician. Something is wrong with the new setup, or there exists a return path other than the return wire. It is true that kitchen, bath, and outside circuits should have GFI circuit breakers, but I don't think they have to be on the same circuit! Each circuit needs protection by GFI, but each circuit may have its own GFI. Doubling up of outlets (not circuits) served by one GFI was done in the past as a cost saving measure. In my house, one outside outlet and the powder room is served by the GFI in the powder room, however, this is only one circuit. My house was wired in 1976. But care must be exercised in the layout to not create potential overloading of any one circuit. I expect codes have changed since then. At that date, GFIs were a new item. The general rule was that GFIs were required in locations where shock hazards were most common. Most of the locations were where one might touch a grounded item and a damaged or mis-wired appliance at the same time. Examples are: an electric fry pan and a metal kitchen sink or faucet; electric shaver and bathroom faucet; a radio dropped in the bath tub; and outside, a faulted device with the user making circuit to earth or a piece of plumbing; etc. Under these rules, places such as living rooms and bedrooms were exempt. However, local authorities may add additional requirements. The instructions for GFIs often state that these should not be used in series. For example, there could be a GFI circuit breaker in the main entrance box that is serving a bathroom circuit, but another small GFI was installed inadvertently in an outlet box in the bathroom in the same circuit. This would be two GFIs in series. If you are located in an incorporated municipality, very likely there is a building inspector and a permit is required to make major wiring installations. If this is the case, your building inspector can be an Allie in getting this situation corrected. In regard to the buzzing sound, have you determined the source? Is it a transformer in an LED fixture that is part of the power supply for the light? Transformers do present design problems and are prone to buzzing. Cheaply or poorly made transformers can be noisy. If this is the source of your noise, the solution is to replace the transformers with better ones, or get better fixtures.

but in general for regular fixtures, the power line goes to the fixture, then the black (hot) wire goes down to the switch and back. That's called a switch loop and while it is common, I don't know if it's more common than having power go to the switch and then on to the fixture. It all depends on the specific layout of the house in question as to which way is better (ie. uses less wire) And while a switch loop will have power still present in the fixture's box, it isn't actually one of the wires that is attached to the fixture itself. Those wires are still just the neutral and the switched hot coming back from the switch. The constant hot is wirenuted (is that a term?) to the wire going to the switch and tucked into the back of the box. No need to touch that if you are replacing the fixture. But as we've all stated, you should still turn off the breaker.