Most of the time. Certain crimes (eg public intoxication) often have an arrest followed by letting the person go when they’ve sobered up, so no official prosecution but not no arrest.
Yeah, but protestors are frequently arrested and charged with completely made up charges. It is just a tactic how to discouraged protests. The cops doing arrests know about it, prosecutors know about it, defense layers knows about it and protesters know about it.
It has nothing to do with deterring crimes or crime rates, it is just politics.
Can you think of any other?