RC vehicles do not use brushless DC motors. Those are usually used in PC fans and other industrial applications. For an r/c motor, you'd be looking at either a 3-phase brushless or a brushed DC motor.

1. You can run an ESC with a transformer so long as the voltage coming out is clean enough. A large capacitor should help assure this.
2. For an electronic speed control, you can't exactly vary the input voltage. They actually look for a pulse wave coming from the ESC. Not a varying voltage.
3. Since you need brushless DC, r/c is not going to work. Maybe a PC fan? Or you could use a Brushed DC motor...

I would suggest simply using a variable resistor (potentiometer) that will handle the current that your motor will end up drawing to vary the voltage. This will end up being your speed control, even though it won't be an electronic unit (pulse signals to the motor), it'll be a mechanical type (variable resistor).
-Eric