Nice summary Jacob. I'll just add a British perspective if that's OK. I don't recognise "put the others to rest" as a way of stating an intention to kill someone (which is weird because I have seen plenty of American movies!) A lawyer putting a case to rest is consistent with UK usage. Similarly, a celebrity who is accused of some scandal might want to "Put the story to rest" by explaining why it can't possibly be true. A nurse saying "put him to rest" is possible but if I was the patient I would be very worried for the reasons Jacob gives: it implies that they are going to be laid to rest soon, because they will be dead. I think in the third case, at least in the UK, it is best to say "put Thomas at ease" or "put his mind at ease", which just means "reassure him". Examples: "Thomas is worried that you might be planning on voting for Donald Trump and that he might have to sever all ties with you. You'd better put his mind at ease by showing him your signed picture of Bernie Sanders" "Thomas has applied for the job of Divisional Manager but he's very nervous. I'll put him at ease by telling him how impressed we were with his CV"

"at the very least" is a longer version of "at least" you say it when there aren't many things left that you can do/ there aren't many options available we don't have a million dollars but at least we have bread on the table. put at rest / put to rest (sounds more natural to me) It depends on the context A bad guy from a movie saying that he will "put the others to rest" he probably means that he will kill them a lawyer that wants to "put the case to rest" he wants to end it once and for all a nurse at a clinic/hospital saying that he needs to be put to rest can mean that he needs a to be put on a bed to rest or in worst case scenario prepare a coffin for him.

To put someone at rest means to give them confidence or make them feel comfortable or at ease. At the very least means the minimum action or the smallest thing that she might do to make him feel good.

It means she wants him to be comfortable