The police officer can only stand over you if you are, say, on the floor.
If he stands by you, he stands next to you.
It would not be usual to replace with with by in this context.
Being saturated with implies its your own blood and that it's not just happened. Saturated by implies that the blood was falling on to you.
The differences are very subtle, but they can influence your understanding of what the writer is trying to say.
Hope this helps.