Why is it dangerous to stand on the edge of platform near the line, when the train is passing by?
This is due to one of the basic concept of fluid dynamics, the Bernoulli's principle!
Imagine you are standing on the edge of the platform as you said. Now the volume of air in front of you is equal to the volume behind you(roughly) and since you dont feel any push or pull in any direction whatsoever right now is due to the fact that the forces, better yet the pressure caused by those forces on your body is balanced. Next moment a train is passing through the station. Now as it goes, it displaces the air in front of it with some velocity v. Now if we consider an area A both in front and back of your body, then according to the equation of continuity, the volume flow rate at any given instance remains constant so:
A1*V1 = A2*V2
Where A1 is the area in front of you and v1 the velocity of the air in that area and the second one being for your back.
Now this means that the area is inversely constant to the velocity through it.
Since the air behind you has almost negligible velocity behind you but that in front is considerable and brought due to the moving train their will be a change in the area for the given volume flow rate, now there is lesser area in front of you. Lesser the area lesser will be the pressure for the decreasing force and so the air pressure in front of you will be less than that behind you.
This is where Bernoulli's principle come into play! Loosely according to Bernoulli's principle, the pressure should remain constant and so the wind blows from the higher pressure that is your back to the lower pressure region that is your front. And this is what causes a push felt on standing close to a moving train.