Yes they do know the trajectories so you put yours in a one where it should not hit anything. Most modern satellites also have engines so they can move on their orbit to dodge stuff if needed. Also remember that space is 3 dimensional so you can be at the same exact "spot" on this map but still be few kilometers apart.

Also this visualization is kind of misleading as it makes the satellites look way too big. In reality you could not even see them from even from the closest zoom available.