How do plasma lamps work?
ANSWER FOR QUESTION 1

Your multimeter is wrong method to measure body resistance. Human body is few kiloohms! When human is electrified - effective impedance is between 1000-5000 ohm (not kilo, not mega!).

IEC says (text from Wikipedia):

The International Electrotechnical Commission gives the following
values for the total body impedance of a hand to hand circuit for dry
skin, large contact areas, 50 Hz AC currents (the columns contain the
distribution of the impedance in the population percentile; for
example at 100 V 50% of the population had an impedance of 1875Ω or
less)

Voltage  5%          50%          95%
25 V     1,750 Ω     3,250 Ω    6,100 Ω
100 V    1,200 Ω     1,875 Ω    3,200 Ω
220 V    1,000 Ω     1,350 Ω    2,125 Ω
1000 V   700 Ω       1,050 Ω    1,500 Ω


See also: Electric Shock on Wikipedia

Human body is not a resistor!!! It's not linear. It contains:


electrolytes and they behave very diffrent at diffrent voltages or currents
cells (biological), some of them act like small capacitors and they conduct high frequency better than just a resistor


Power able to stop human heart or cause ventricular fibrillation may be less than you think.



ANSWER FOR QUESTION 2

Im not sure if this is what you want. This is very simplified equivalent circuit for plasma ball and human:



(sorry for bad image quality, I have only paint on this notebook)

If you calculate voltage on resistors - you will realize that guy with a mustache gets very small voltage. Most of it is on resistor representig glass resistance. Im not sure how big glass resistance may be (depends on glass type, thickness etc), but im almost sure thats more than 1Gohm. If someone think I'm wrong - please leave comment, I will correct that.

At 30kV, 1Gohm glass resistance and 10k body resistance - you get only ~3 volts and current is ~3uA.

However human is not a resistor, and glass works as capacitor. For high frequency that changes impedance a lot, and glass impedance will be much less for higher frequencies.

On my schematic capacitor is completely unknown, because it's very hard to determine it. It depends on how much skin surface is touching glass.

Capacitor impedance is inversely proportional to frequency.



ANSWER FOR QUESTION 3

I think it must be frequency high enough to pass current thru glass (as I mentioned earlier - it acts like capacitor). Plasma is one electrode, glass is isolator and your finger is another capacitor electrode.

Capacitors have low impedance at high frequency, high impedance at low frequency.



SHORT ANSWER FOR QUESTION 4

Grounded part is shown on schematic (this is simplified!)



SHORT ANSWER FOR QUESTION 5

This is relatively safe because there is a glass between you and 30kV source. As I mentioned before - it's a capacitor and very high value resistor conected in parallel. You can calculate current or voltage on human body if that "glass resistor" was 10kOhm instead of 1GOhm.



SHORT ANSWER FOR QUESTION 6

Playing with kilovolts is always dangerous. 

However 15-30kV at 1-5kHz from very low power transformer should not hurt you if there is glass thick enough between your body and plasma/electric arc.