Theoretical questions about potentiometers

Hello everybody!

I need help with potentiometers, because this page discusses this topic on several pages, but I've got further and further questions.

First of all lot people says, that you can not use a potentiometer in an AC environment, because normally the potentiometers are designed with low power rating. Even if I have a 100Kohm linear potentiometer, if I use this with 220V AC, still means 0.484W which is too much if I have a potentiometer with max 0.2W power rating.
I say ok, but theoretically, if I use only 9v AC, is there any obstacle to use my potentiometer in AC environment?

Secondly, I have seen a normal room lamp without a normal 2 position switch, but with a switch like a linear potentiometer which is very similar to a drawings can be found on: http://www.allaboutcircuits.com/vol_1/chpt_6/1.html (second coloured figure). Is there any chance that the AC lamp I've seen used this potentiometer or rheostat technic written and taught by this page? Or do these lamps using something different technology to control the strength of the light? If yes, what is the name of the technology?

And last but not least I have a theoretical question. If I have a voltage divider circuit build with a 100Kohm potentiometer, I can divide the voltage with the rotary switch. Suppose, I set the rotary switch to have about 6.75V from 9V battery. It means 75% voltage drop for the first two terminals. But this means also, that I use 75Kohm resistance from the 100Kohm.
Now, I want to put a light bulb into this 75% branch. What if the light bulb's resistance is much smaller than the 75Kohm potentiometer resistance? Theoretically, it means that I "shorted" the branch, and the potentiometer created 6.75V branch has no more 6.75V. Is that correct? If yes gives the light bulb any light?

 

Very useful answer, Thank you!