I am guessing by the question you want either of these stats to be able to start the furnace, without using a relay. As long as you are using the same control power supply for both the answer is yes. Use the same connections on both if that is what you are trying to do.
The use of a four way switch is needed when a load (such as a light) needs to be controlled from 3 locations or more. For instance when you walk down a hallway and there is a light there are probably at least two switches one at the beginning of the hallway and one at the end. These two switches will turn the light on or off from either location. These two switches will be three way switches. When the need to control a light or a load from more that two locations arises a four way switch is introduced. A light or load can be controlled an unlimited amount of locations by adding four way switches which are wired in between the two three way switches. Think of a sandwich where the three way switches are the bread and the meat and veggies are the four way switches. You can put as much meat and veggies as you want, but you always need two slices of bread on the top and bottom.
They are used as a hard wired equivalent to binary switches for digital ID purposes along with enabling enabling optional PWB circuitry in various electronics that are not functionally included in a standard product but has the circuitry installed in the PWB.
It may run. But not efficiently or to capacity as there will probably not be enough air flow.You also run the risk of ruining the compressor by flooding it, as residential a/c units are notorious for not having hi and low pressure cut-out switches.
You likely wired it wrong. Not sure what you mean by "fizzle out".
by turning the control switches to the on position and attempting to light the furnace.
They are wired in parallel, series and series - parallel.
No.
The gas valve is an electrically powered device that is wired at the end of a series circuit so that it can only be energized (open) if all of the safety switches upstream in the circuit are closed and the pilot flame is lit on a standing pilot furnace.
Yes.
how to connect cables to switches 240 box
It is dependant on whether the switches are in wired in a parallel or series configuration. If the switches are wires in parallel then both switches would have to be off to turn the light bulb off. Either switch could turn the light bulb on. If the switches are wired in series then both switches would have to be on to turn the light bulb on. Either switch could turn the light bulb off.
Deadman or failsafe switches. Think of them as an and gate logic circuit...all switches must be on (1) in order to power the load (1).
The output of an AND gate is set only when all of its inputs are set, and when switches are wired together in series, current can flow only when all of the switches are on.
Most buttons are just momentary switches hard wired.
In control circuit wiring the safety switch is in series with the holding coil.
Your thermostat or condenser is wired wrong on the control side. Usually there is a terminal inside your furnace that has the same connection colors (Y, W, R, G, C) as your thermostat. It should be connected color to color to the thermostat with the 2 wires from the condenser wired to Y and C.