Technically, you could use a non-grounding switch if you can find one anywhere. But the safest method is to run a new circuit containing a grounding wire to the switch box and use it to safely ground the switch.

Can I use a 120 volt rated switch on a 240 volt circuit if I only switch one of the hot legs?

No, this will not work. Although each leg of a 240 volt single-phase circuit measures 120 volts to ground, they measure 240 between each leg. Once the switch is turned on, you no longer have 120 volts present, but 240 volts instead, which will most likely cause the switch to fail.

I was changing a light switch with the power on when it sparked. Now everything on that fuse has no power. The fuse checks out OK. What could be the problem?

Did you check the fuse with a continuity tester or only visually? Many times fuses blow and they don’t appear to be bad when looking into the glass window. If the fuse was bad, was it replaced with a known working one?
If the fuse is definitely good, then you need to start searching all the devices on that circuit for a loose connection that may have become worse when the spark (overload) occurred.

I recently replaced a three-way switch at the bottom of my stairs. Now when I flip the top switch the light turns off, and I can turn it on and off by flipping the bottom switch. But when I flip the bottom switch to turn the light off, I can’t turn it back on with the top switch. I thought I wired the replacement switch correctly!

It sounds like you got a common wire mixed up with a traveler wire. There are some diagrams available that may help you to solve this problem on our website at www.wurtsboroelectric.com/switchquest.html.
The most important thing is to identify the common wire and make sure it is connected to the common terminal of the light switch. The other two wires only determine position of switches when the light is on or off.

I have one switch in my kitchen that controls two lights. Is there a simple fix to have two switches so they are controlled independently without fishing wires?

If wires from both lights are home run to the switch box; that is, not wired from the switch to one light, then from that light to the other light, then you could replace the switch with a duplex or stacked-style switch (two switches that fit in the space allocated for one) and control each light independently.

I’m replacing a single pole switch that controls a ceiling light. It gets power from the light fixture and loops it back. How can I replace the switch with a combination switch and outlet so that the outlet is always live and the switch controls the light?

You can't do it without running an additional wire to the receptacle location for constant power. Either an additional 2-wire cable or replace the existing with a 3-wire cable of the appropriate gauge.