In response to OP's questions: Yes and Yes.
Missouri Revised Statutes
Chapter 301 - Registration and Licensing of Motor Vehicles §301.130.
5. ... Each such
plate shall be securely fastened to the motor vehicle or trailer in a manner so that all parts thereof shall be
plainly visible and reasonably clean so that the reflective qualities thereof are not impaired. Each such plate may be encased in a transparent cover so long as the plate is plainly visible and its reflective qualities are not impaired. License plates shall be fastened to all motor vehicles except trucks, tractors, truck tractors or truck-tractors licensed in excess of twelve thousand pounds on the front and rear of such vehicles
not less than eight nor more than forty-eight inches above the ground, with the letters and numbers thereon right side up. The license plates on trailers, motorcycles, motortricycles and motorscooters shall be
displayed on the rear of such vehicles,
with the letters and numbers thereon right side up.
Chapter 307 - Vehicle Equipment Regulations §307.075
1.
Every motor vehicle and every motor-drawn vehicle
shall be equipped with at least two rear lamps, not less than fifteen inches or more than seventy-two inches above the ground upon which the vehicle stands, which when lighted will exhibit a red light plainly visible from a distance of five hundred feet to the rear.
Either such rear lamp or a separate lamp shall be so constructed and placed as to illuminate with a white light the rear registration marker and render it clearly legible from a distance of fifty feet to the rear. When the rear registration marker is illuminated by an electric lamp other than the required rear lamps,
all such lamps shall be turned on or off only by the same control switch at all times.
2.
Every motorcycle registered in this state, when operated on a highway,
shall also carry at the rear, either as part of the rear lamp or separately, at
least one approved red reflector, which shall be of such size and characteristics and so maintained as to be visible during the times when lighted lamps are required from all distances within three hundred feet to fifty feet from such vehicle when directly in front of a motor vehicle displaying lawful undimmed headlamps.