Right. The farthest people have been is the Moon, which is still gravitationally bound to the Earth. Plenty of spacecraft have been out of Earth's gravity well, and also a car, but no humans.
What do you mean? I thought the car had an astronaut suit in the drivers seat containing the dessicated corpse of the real Elon Musk, after being murdered, memory-absorbed, and doppelganger-ed by the current version.
You would never escape the influence of Earth's gravity, as far as I know.
From what I understand everything in the universe has a slight gravitational effect no matter the distance, it's just that the effect get infinitesimally small, but never reaching zero.