Electronic – Permanently dimming an incandescent light bulb

For Q1: (a/b) are both sort of correct. A dimmer should never be a variable resistor as that would consume a large amount of power and would cause fires or fail easily. Dimmers are made from SCR's which are active devices which save power and don't heat up nearly as much. So long as the dimmer is rated to handle both lights, then it shouldn't dim when the second is turned on.

"Modern dimmers are built from silicon-controlled rectifiers (SCR) instead of variable resistors, because they have higher efficiency."
http://en.wikipedia.org/wiki/Dimmer

On the other hand, the rest of the circuit (wires) will have to carry more current when the second light turns on. If the wires aren't large enough they'll heat up causing a slight increase in resistance and a corresponding slightly lower amount of current to reach each device.

For Q2: (a) is correct. The dimmer will be wired in series with the lights/switches so lightning would still have to travel through the open (off) switches to damage it which is the exact same even if the dimmer is wired after the switches.

You look golden to me.

An 82 ohm resistor would dissipate about 175 watts; indeed, a 15 watt bulb may dissipate that much power briefly. Something the size of a 15-watt bulb that dissipates 175 watts is going to get very hot, however, and when tungsten gets hot its resistance increases by an order of magnitude. You may have been expecting your 1K resistor to dissipate about 1.5 watts, but in practice it would have dissipated about 17.5 initially. Most resistors don't nicely increase their resistance with temperature the way a lightbulb filament does, however, so your resistor may have continued to dissipate that much power until it melted, whereupon its resistance might have actually decreased, causing it to try to dissipate even more power, until things went downhill very severely.

I would suggest that you might consider a Christmas decoration that's designed for a C7 bulb; such bulbs draw about 1 Watt. If you wanted to use a resistor that drew less power, two 33K resistors half-watt resistors in series would probably be reasonably safe if they were somewhat ventilated (the resistors should dissipate less than 1/8 watt each, but half-watt resistors should be used so that in case one fails shorted the other would be able to handle the 0.44-watt fault power) but might not let through enough power to operate the touch switch (if it does work, keep adding 33K resistors until it doesn't work reliably, and then remove one). The fact that incandescent bulbs have a much lower resistance when cold than when heated allows a much smaller energy-wasting element to be used for a given application than would otherwise be necessary.