You should be able to plug in motors and a battery directly to the receiver. A data sheet or schematic will always be helpful.
Both sets come with a transmitter and receiver and by the photos I think the transmitter is the one with the push buttons. You control the receiver via the transmitter using the push buttons. IMHO no software programming needed.
A motor driver is required if you are connecting motors to a robot or to I/O pins of an MCU. The MCUs I/O pins can only deliver a mere milliamps while a motor will require maybe several amps. Trying the drive a motor directly though your MCUs I/O pins won't turn the motor or possibly fry your MCU. Input of a motor driver is a signal from the MCU, this input drives internal logic in the motor driver which drives the motor.
Yes they limit the number of motor connected because its what's the circuit was designed for. You will see motor drivers with 2channels or more. These channels are what the motor driver can control separately. Connecting 4 motors to a two channel motor driver is a no-no. You risk overloading the motor driver.
Please do a search of the website there are numerous topics discussing this in the member tutorials.