I am considering a sea level aerodrome with high temp and low pressure.
The tapeline height of the aerodrome (sea level in your instance) largely is irrelevant as the aeroplane doesn't have a tape measure. What counts is Hp and OAT (both of which the aeroplane understands) and which define the performance heights (ie Hp and Hd). For takeoff and the like OAT is important in its own right as the jet engine is quite sensitive to OAT - far more than for the piston powerplants.
You will have a longer run because there is a lesser amount of air
No .. going faster is what does the trick. That is related to the higher Hd's giving you a higher TAS ... but "lesser amount of air" should have been left behind after your first pre-solo briefing ...
you're having a higher power setting
at idle ? .. or am I missing something here ?
while using reverse thrusters.
not relevant for scheduled distance.
In the real world, for normal conditions, reverse largely is for the pilots' amusement - brakes are where it all happens - unless you are on a long runway and choose not to use brakes. On the other hand, contaminated/wet runways are a different animal if the brakes are near useless.
You will have a shorter run because the performance of the engine and aircraft is already low.
fanciful nonsense. Landing performance principally is due to the brakes and the interaction of brakes and speed .. the engine doesn't have much to do with it.