The Earth has a full atmosphere with winds, an expansive array of magnetic and electric fields, and a much much higher gravitational pull then Mars or the moon. About a factor of 10 removed from mars and about a further factor of 10 removed from the moon.
You'd obviously need more fuel, and fuel that can burn in a completely different atmosphere then it's intended to run in. It's an invalid test for the kind of useful metrics that would be obtainable in a "pure" vacume out in space.
Rockets carry oxidizer along with fuel, so the composition of the local atmosphere doesn't really figure. Also, your factors are way off; Martian gravity is a bit shy of 0.4g, and lunar gravity a bit proud of 0.1.
Finally, we don't need to land on the moon, or Earth, or anywhere else, to validate a method of landing on Mars, because we already know how to land on all of those things. We've done it plenty of times before, in all cases; the difference between doing it manned and doing it unmanned is purely one of mass.
We've only landed light things on mars, curiosity is the heaviest at 889kg, and the methods used don't scale easily.
Anything that can sustain humans for an extended period of time is going to weigh a lot more. EDL (Entry descent and landing) is a solvable problem, but it's not a solved one. You can find lots of recent work on it by googling that term.
Not to disagree that we can test on Earth better than the moon. Mars has a light atmosphere, but it doesn't have no atmosphere.
I wonder if there's an altitude you could do a "landing" at that would be thin enough atmosphere and weak enough gravity to get close to Martian conditions.
NASA does indeed use high-altitudes on earth to test Mars aerobraking, atmospheric entry, and supersonic parachute deployment[0]. For the actual terminal descent and landing speeds are low enough the atmosphere is not significant, you can just test that at sea level.
Gravity will still be too high, gravity at the ISS is 0.89 times gravity on the ground and you obviously need to be lower than that. But it's definitely the closest we can get to a large scale martian atmosphere.
You're wrong about the gravity. The escape velocity of Mars is 5 km/s, half of Earth's and twice the Moon's. The surface gravity is also .4G which is about half the Earth's and two and a half times the Moons. So they're all a lot closer together than you said.
