According to Newton's 3rd Law, every action has an equal and opposite reaction. In order to walk, the ground must exert the same amount of force you put on it and you must have friction. The Flash must have friction in order to go super fast. One of the supervillans he must fight is Captain Cold, who shoots a layer of ice in front of him, rendering him unable to get any friction on the ground, and unable to use his super speed.
In order to walk across water, the water must move out of your way. If a liquid has a higher viscosity, it requires more energy to move it out of the way. The Flash is able to run faster than it takes the water molecules to displace and move out of the way, so therefore he can keep moving on top of them. The water acts more like a solid than a liquid at these speeds, you can see this by slapping a pool of water really quickly.
For The Flash to catch bullets, he would need to speed up to match the bullet's velocity so the net speed between him and the bullet is zero. He can then easily pick the bullet out of the air and save the innocent bystanders.