Well homemade might be a little difficult but if you buy one for parts or repair you could find out what the problem is and fix it.
By a motor
a battery and a toy car..........................
With electrical wires after checking that the panels output voltage is compatible with your car.
NO
Rubber band car
There are many toy car companies that make toy car garages suitable for younger children. Some of these companies include Matchbox, Hotwheels, and Little Tikes.
you can make a toy car move with a ballon and pump by blowing balloon up and leting the pump go
Keep the batteries charged up.
you push it
Toy car
a toy car weighs 500gms or more than that depending on the make