>What makes landing on the Moon so difficult is the number of variables to consider
Compared to Earth, surely it's easier. Less terrain difference, lower gravity. It's getting there and the remoteness is what makes it hard.
What happens when you over-compensate with the thruster?
Sometimes you can recover from that, sometimes not.
Anyway, the easiest way to get a feel for these things is to play some Kerbal Space Program. Try doing some moon flights. You'll quickly realize that the part of the mission that feels easiest on the home planet (landing) also feels the hardest on atmosphere-less bodies, and vice versa (e.g. taking off, or slowing for landing).
Managing delta-v is half of what makes a Moon landing require precision. An atmosphere can let you ignore this half to a degree (depending on specifics of vehicle/mission).
Not quite. You can compensate with a landing gear that can survive your terminal speed going to zero very quickly and absorb the extra energy.
The math is much simpler on the Moon because there is no atmosphere.
Mars is probably the worst of both worlds, you have a thin atmosphere that is a nuisance but not very good for braking.