The officer found everyone dangerous.

Both are grammatically correct, but since the two sentences describe essentially opposite conditions, I don't see that grammatically one might have a preference for one or the other.

The second sentence is a little ambiguous; it could mean the officer found all the dangerous people, or that the officer found all the people dangerous - two very different things.

1. The police officer found nothing dangerous.
2. The police officer found everyone dangerous.

Are both grammatically correct, and is #1 your preferred choice?

How can we choose between? They do not mean the same.

(1) is grammatically correct, depending on context of course! (Where? when? why?). It means that the police officer did not find anything dangerous.

(2) is in correct word order, etc, but does not really mean anything. It might mean "The police officer found every person who was dangerous." Or, it might be trying (unsuccessfully) to mean "The police officer thought (or had the impression that) every person was dangerous".

In English, you can use the verb "to find" to mean "to discover personally" for example

I found John very friendly.
I found my hotel room very cold.

But you would not "find" something "dangerous" in that way. Scary, maybe.

In the first sentence the verb "to find" is being used literally. Or at least it would be interpreted that way. He looked in your bag. He found nothing dangerous.

In the second sentence the form of the sentence suggests it is being used metaphorically, to mean "to receive an impression". One "finds" things to have subjective qualities, not objective ones.

So the police officer might find a person or persons threatening or frightening (which are subjective attributes), but he could not "find" them "dangerous" in that way.

You could say (or write)

(literal)
I did not find my keys.
I found $20 in my pocket.
I found a cat in my house.

(metaphorical)
I did not find John friendly.
I found Germany interesting.
I find brandy makes me sleep
John found Italy relaxing.
The soldier found war horrible.
I find grapefruit very bitter.