So, it's sentence. I know you technically can't hear the n but it's there. If you add "be" you're saying the police haven't done the finding of her yet. So you would have to bring "find" in present tense since "is" is in the present tense, like "The police is going to be finding out who killed her." As in saying, they have not started yet. Whereas saying, that I think would be more correct, "The police are going to find out who killed her." or present, "The police is going to find out who killed her." This is saying that the police are in process now of finding out who killed her. So, with be: if you add be, find must be turned to finding. They haven't started finding out yet. Without be: Police are in the process of finding out. (I would say this one is more commonly used. The other one still seems wrong to me even corrected.) I hoped that helped. XD

Other: it's mainly used to differentiate people or things from something already talked about. Example: "I don't want that cookie. I want the other cookie." Another: Think of it as an addition to something, like add one more of something already talked about. Example: "I want another cookie." The others: Think of this one as, "those that weren't already mentioned in the group." You're trying to differentiate from things, people or places that have already been mentioned. For example: The others were late to the field trip, so they had to stay at the school." What makes this different from other is you're talking about more than one thing, person or place as you would with other. Others=more than one thing, Other=one thing

They all kind of carry the same meaning that something is really bothering you. However, I don't think they're as common to be used frequently. They're definitely sayings that you would only use around people you trust, because there are only used when something is very troubling. To me, they're phrases not taken lightly.