You're actually right - parachutes *don't* work well on Mars. That's precisely why they have to use a sky crane with thrusters to slow the descent of the lander. Shortly before the heat shield separated, the lander was traveling at over 200 mph with the parachute completely unfurled. Earlier landers used an airbag system to cushion their landings. There just isn't enough atmosphere for a parachute to work as well as it does on earth.

Once down, the rover is largely autonomous in its movements, maybe similar to a self-driving car in some ways, but it does communicate and receive instructions from earth via the Mars Reconnaissance Orbiter, which orbits Mars and relays signals between the rover and earth. The rover can't contact earth directly.

The fact that the drone will fly in an atmosphere 1% as dense as sea level on earth *is* amazing. It may not even work, but they tested it in a specially built vacuum chamber on earth and it worked in there, so hopefully it translates. It's pretty light (~ 5 lbs) and has large rotor blades for its size that I'm sure spin very fast. If you want a more detailed explanation you'll need a physics major or an aerospace engineer to weigh in!