Well, you do what I do with any electronics I create, place it on some ventilated area where fire can't spread, have long cables with switches far from the equipment, do any work with power off (after waiting for any capacitor discharge), and wait for the "tshhhhh" every so often.

After it is well tested (measuring temperatures is hard, but doable) and you are confident it works, you can use it normally.

No worries. Looking at the sine AC wave should be fine. If you get a "10X" probe or one that has a 1X/10X switch, what happens in 10X mode is that the voltage gets divided by 10 through a resistor, so your multimeter should see 22V RMS sine wave (peak value should be 31V).