The blue lines on the hill are to give an athlete depth perception.
answer 2:
I think you're asking about the dye sprayed on the snow? This is applied after the course is iced down and before the race begins and is a visual aid in case the light goes flat. It approximates the line the racers will take and gives them terrain definition. It is more common to Downhill and Super GS, though, than it is to slalom. At those speeds on an overcast day, you might think you're still a few feet in the air when suddenly OOF!, you're hitting the snow before you were ready to absorb. Conversely, you might not be able to tell when there is a rise or dip in terrain and you get thrown or compressed. On flat days, to humans, the horizon becomes the same color as the snow, Blue is the color that works best both peripherally and near distance.
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There are no panels (flags) in slalom unless you are talking about paneld slalom, GS (giant slalom), super G or downhill. They do not have a meaning but to tell the racer which gate to ski around next.
They are used primarily for low light conditions. Prior to the blue marks they used pine boughs to help the skiers judge where the ground is (depth perception, and terrain orientation).