Earlier quoted context omitted.
No. If the Earth's mass were to vanish, the Moon would continue to orbit the Sun. It would be a bit more wobbly, but the Earth is not an essential part of the system. If the same happened to Jupiter, all of those moons would fly out of of the solar system. (Or at least go cometary.) None of the orbits would survive.
I don't see how this and Kepler's laws fit together. The moon's mass is significantly different from the earth. How could the moon have the same orbit as the earth if the earth wasn't there?
the period and orbital velocity are dependent on the mass of the orbited object and the radius of the orbit.