12V switch in series with two 12V DC motors & 24V power supply. Is this ok?

Don't think much of your series motors idea, too many possible problems. Voltage does not run through the switch. When the switch is off, 24v appears across it and when it is on, zero volts across it.

 

I second that...
Motors are not a simple 12V device... They are dynamic. If one motor is seeing a greater load than the other, the voltage will no longer be split evenly. There is a high probability of one of the motors seeing a higher voltage than the other. I can't say "don't do it", but be mindful of how you are loading the motors.

Now... let's discuss voltage and current a little...
Voltage does not run through anything... it's present 'across' something... in that from one terminal to another, the voltage is present. Current run's through things... and it's the relationship between the voltage across it, and the resistance it presents that determines the current through it.
What are your motors rated for? Everything in a series circuit passes the same current... so if both motors draw 500mA then 500mA *must* also pass through the switch when it is running. When the switch is open, there is no current flow, and the *entire* source voltage will be present across the switch.
So, please size the switch to a higher voltage, and check the motor ratings to make sure the switch can handle the current.

Running too high a voltage on anything could allow sparks to form while the component is turning on/off, or could allow an arc from one component to another! (Worst case)
Running too high a current through anything can cause it to heat up. Excessive heat leads to damage, and/or smoke & fire.
!! It's important to note, that increasing voltage also increases current !!
A switch should only ever be on or off though... so the current through a switch will almost always be decided by what else is in series with it...

 

48V in series will most certainly cause it to spin much faster!
You have gone from providing 12V to each motor, to providing (in theory) 24V to each motor... but it may not have been an equal 50-50.

A 12V motor and a 24V motor are far from equal...
If they are selling them as two different descriptions or items, they are fudging numbers! Very bad...

An increase in voltage will equal an increase in speed of the motor.
An increase in current will equal an increase in force of the motor...
Tricky thing though... If the motor does not have the force required at the specified voltage, the only way to increase the current it to buy a different motor, rewind the coils in the motor, or increase the voltage...
Voltage and current are related.
So.. to solve you dilemma, if the motors are 24V safe, then you can use anything 24V and below. You may need a different power supply for this. Look into PWM motor controllers as well. You can use them to vary the power to the motor.
There may not be a happy medium though... a motor without load will always go faster than one with a load... so you may have to settle for a weaker motor that runs a little slower if they will see a varyation in load

 

1) This depends entirely on the motor design. The motor should indicate it's designed RPM, *or* it's RPM per volt. 2) Again, depends entirely on the motor design. The 24V motor may be designed to draw very little current. You should look for the motor's torque rating or *power* handling capabilities.
3) You are correct in thinking they gear it differently, or use different motors.