The Sagan is based on the Space Shuttle - it has two boosters to help launch it and a large external tank that feeds its 3 onboard engines.
Once these are all jettisoned, they only have orbital manouevering thrusters, which might possibly be able to allow the craft to land, but are nowhere near powerful enough to launch the vehicle from the surface of Mars, even with its lower gravity.
The Sagan is based on the Space Shuttle, which was only designed to reach Earth orbit. Even allowing for some design changes, at the time it reaches orbit it has jettisoned the external tank. This feeds the 3 main engines, and without this tank, there is no source of fuel for these engines which would allow it to increase its speed from 5 miles per second for Earth orbit to the 7.5 miles per second needed for an Earth escape trajectory.
In the animated graphics at the very start of the film, Mars is shown rotating in the wrong direction.
During the meteor shower the impacts are from reasonably-sized rocks that have bright glowing trails all the way down to the surface and cause substantial impacts, which can be heard along with their descent through the atmosphere.
Yet meteors that hit Mars wouldn't be that different from those that reach Earth.
1) These are mostly no bigger than a grain of sand.
2) The vast majority completely burn up in the atmosphere.
3) Any fragments that do reach the surface would make no sounds in the incredibly thin atmosphere of Mars.
4) Even on the Moon - which has no atmosphere - the astronauts' multi-layered spacesuits were designed to provide protection against micrometeorite impacts.
The external tank is seen being jettisoned at the same time as the two main boosters. As the tank feeds the 3 liquid-fuel engines, that means the craft would no longer have any thrust, and would fall back to Earth. The tank provided fuel for the space shuttle for a further 6 minutes to enable it to reach orbit.
The private backers of the Mars mission plan to turn a profit on it by importing diamonds and other precious stones rare to Earth but common on Mars. But according to the law of supply and demand, flooding the market on Earth with gems from Mars would drive DOWN their price.