When temperature increases what happens to the air molecules and aircraft while landing and takeoff during hot weather?
If all else is equal, an increase in temperature will result in a decrease in density of air molecules. To fly, a wing leverages these molecules, so the aircraft will need to fly faster to generate the same lift. Therefore the takeoff and landing distances are increased. 

Engine performance is also impacted. Most engines outside of NASA breathe air and so perform better when that air is dense. Jet engines also have a maximum exhaust gas temperature they can withstand, and in very hot temperatures the amount of thrust they produce needs to be lowered so as to not exceed that value. This is the basic premise of how Airbus ‘assumed temperature’ works, where the pilots tell the engine that the temperature is hotter than it actually is, so the FADEC automatically caps the thrust.