Assumption 1: Landing a spaceship softly takes the same rocket burn as it it does to launch it.
Assumption 2: You are envisioning this spacecraft taking off and landing like Saturn V. I'm only going to calculate the taking off/landing part.
Assumption 3: The spaceship has the same density as a Nimitz carrier. Estimating this ship at 5 times the length and 10 times the diameter of a carrier, the mass will be roughly $5\cdot10\cdot10 = 500$ times greater, or 50 million tons (5e10 kg).
Assumption 4: You can scale a Saturn V up linearly by strapping a whole bunch together (which is what your picture looks like). I'll only compare to the first stage, since you seem to be interested in the blast damage to the planet.
Assumption 5: Ignore fuel requirements. Logistics are for professionals, we're perform calculations on things that go boom.
If the Saturn V produced 35MN to lift off 3e6 kg, then you need 5.8e11N to lift off 5e10 kg, or half a teraNewton, if you like to use units that not many people talk about. Energy is force times distance, so if we say (another assumption) that the rocket affects the earth until it is a mile in the air, multily 5.8e11 N by 1500m to get 8.8e14 J of energy release.
Lets stack few more turtles to stack on this pillar of assumptions. I'm going to use a conservation of energy estimate to see what all this energy release would do.
This site says that 30% of that energy is released as waste heat. Lets say all that heat is transferred to the sand: the sand just got 2.63e14 J hotter.
The accepted answer here says that it is 1.5 MJ to turn a kilo of sand into glass. That means we can melt 1.8e9 kg of sand. At a density of 1400 kg/m$^3$, that means we melted 125000m$^3$ of sand. Make that a perfect half-sphere and you have about a 40 m^3 sphere of sand. So that would be a significant environmental change.
Lets take those other 70% of energy and convert it into wind energy to simulate a blast wave. That is 6.1e14 J of energy. If we give all the air in a 40 m$^3$ radius, to a height of, say 10m (to simulate a shockwave along the ground) that much kinetic energy, how fast would it be rushing outwards? Well that is a volume of 5e4 m$^2$ of air, with mass of 6e4 kg, so it would pick up a velocity of 141047 m/s. Holy smokes! So the blast wave would probably be more damaging to your safety than the heat.
Lets solve for the distance you need to be to get the air speed down to 50 m/s, which is strong, but unlikely to kill you. I calculate 112 km. Seems high. Lets raise the height of the shock wave to 100m: now we're at 36 km.
Ok so that post will not hold up to any scrutiny, but I can guesstimate your answers as:
1.What are the immediate effects on the surrounding area if such a craft landed?
Anything withing a kilometer is probably killed by heat. Powerful shock wave up to 10km, hurricane force winds beyond that.
2.What would happen to the desert below? would there be any significant changes to the environment due to such large rockets heating everything up/ large object touching down on the ground?
Yes, there would be a lot of glass.
3.What would be the max distance you would have to be from the landing to survive?
The max distance would be the opposite side of the planet. The minimum distance would be somewhere from 10-50km.