I assume you are referring to a residential electric panel. The amount of amps has nothing to do with the voltage. They are independent. A typical residential electric panel will have 120 V. That is the easy answer. Usually there are two hot feeds with 120 V to ground. Between the two hot feeds will be 240 V. The bus bars are arranged in the panel so that when you plug in breakers they alternate between the feeds.
In the United States, a lighting panel, which is any panel that contains branch circuits for lighting and usually receptacles, is limited to 42 circuits. Your panel must be rated for the number of circuits you use. There are a lot of panels that hold nowhere near 42 circuits; some hold only a handful.
240 V
240 volts
Yes, the wire size has to be increased. The existing 100 amp service will now probably have a #3 conductor with an insulation factor of 75 or 90 degrees C which is rated for 100 and 105 amps respectively. Increasing to a 150 amp service will use a #1/0 wire size. If you are thinking of an upgrade, skip the 150 amp service and go to a 200 amp panel. New homes are installing 200 amp 42 circuit panels. The extra cost is only reflected in the materials as the labour costs will be the same regardless whether a 150 amp or a 200 amp panel is installed. The wire size for a 200 amp panel is #3/0. With an insulation factor of 75 or 90 degrees C the rating is 200 or 210 amps respectively.
AWG # 3/0 copper.
A 200 amp service panel with a 60 amp sub-panel.
The formula you are looking for is I = W/E. Amps = Watts/Volts.
Judging by your question I'm going to take a guess and say you should probably not attempt to do this yourself. Nor do I recommend it. That being said. You can either have your service upgraded to 200amp, and install a 100amp double pole breaker and branch it off into a 100 amp sub panel. You could most likely re-use your old panel for the 100 amp sub panel. Or... You could have your new 200 amp panel installed in a different location and your current panel wired into it for 100 amps.
As many as you wish, as long as you do cross 200 amp limit
No, the generator must output 220 volts which any generator I have ever seen does.
No. You can not buy a 200 amp that only occupies 2 slots on the panel.
No. If device draws 200 amps breaker will trip.
There are two things to think about here. First of all a 200 amp breaker will not physically fit into a 100 amp panel. This is so designed because the panel buss is not designed to conduct 200 amps before the current is cut off. A 100 amp rating on the panel is the maximum amount of current that the manufacturer states, that can be handled safely. Second if the 200 amp breaker is in the main panel then everything downstream from that breaker has to be rated for 200 amp conductivity. The wire size will have to be 3/0 from the breaker to the first over current device in the sub panel which will be the sub panel's main breaker. The sub panel can not be a load center but will have to be a combination panel. I doubt that the 100 amp sub panel's main breaker lugs would be large enough to connect the 3/0 cable.
The formula you are looking for is Watts = Amps x Volts.
8 AWG copper is rated for 40 amps. Over 150 ft, at maximum current, the voltage drop would be about 3.76 volts. Using 6 AWG would have a voltage drop of 2.36 volts with the same 40 amps.
100amps
Some 200 amp breaker panels are made with only 20 slots.
Check the nameplate on the service panel. There it will tell you what the buss capacity is. On a 200 amp service nothing in the wiring configuration is allowed to be less than that the service rating. In the market there are 200 amp 42 circuit distribution panels.
Ohm's Law states Volts = Amps x Resistance. You would need to apply 600 volts across 3 ohm load to have 200 Amps flow in circuit. Not sure what you are really asking and why you mentioned 2 gauge.
Depends on where you live in the world. North America it is 120/240 volts. In new installations these days a 200 amp capacity panel is quite common.