This is a rather authoritative way of stating categorically that you don't want something to happen generally or habitually, instead of just one time. The key is the progressive - which makes the prohibition somewhat habitual, as if thwarting the onset of a habit or tendency you want no part of.
For example, in the last example, the speaker could be talking to his son, who just got a car and has been home late a few times. Or a daughter that has started dating. Saying just "I don't want you to come home late" could be used for one occasion = tonight, after the prom, etc.
Having said that, the same father could say "I don't want you coming home late" in reference to one occasion, and it is merely a very authoritative restriction, and still carries a meaning of "tonight or any other night."
In (1) and (3) the speaker doesn't want these to become a regular thing;
In (2) the speaker wants him to cease ALL inquiries - "stop asking around!"
In (4) the speaker doesn't want the fact that the listener has a broomstick to become common knowledge.
This is a complicated quote, because the character is not able to speak directly or honestly to the people in the room. It becomes more clear if we simplify it, and add the implied context:
My son had to leave the country [because he shot a corrupt policeman
who was working for one of you] and I have been busy making sure he
could return. [I would never accuse you of plotting to harm my family,
but] Under the circumstances, I will blame you if anything at all
should happen to him.
But, [putting my promise to enact bloody revenge on you] aside, I will
not be the one who breaks the peace.
A more direct conversation might be to say "Sure, we've been at war, but now we're at peace. If any of you knuckeheads decide to get payback on my boy, I will personally end each and every one of you. Having said that, I'm willing to accept the terms of peace."
The author is using "but, that aside" to say that what came before should be ignored for the moment. For another example, consider a conversation:
"Would you like to go see that new movie? Julia said it was really
good."
"Julia stole my lunch last week and I'm still mad about that.
But, that aside, I do want to go see the movie."
It's interesting to note that putting something aside is not the same as forgetting about it. It is similar to "putting it on the back burner" or "tabling that for now" - it is implied that it will be important later, but not right now.
Best Answer
These are lyrics from "Memories", a song by an American pop-rock band called Maroon 5. The differences:
'Here's to...' is a conventional way of proposing a toast (an expression of good wishes or respect for someone that involves holding up and then drinking from a glass of alcohol). Example: Here's to Grandfather, on the occasion of his 90th birthday! (everyone raises their glass and typically says loudly, '[to] Grandfather!').
'Cheers!' is normally said alone and is a friendly expression said just before you drink an alcoholic drink. Example: some people are about to start drinking together. One says 'Cheers!' (just that) and the others repeat 'Cheers!' and may raise their glasses or just pick them up normally and start to drink from them.
Although dictionaries generally define toasts in connection with alcoholic beverages, people drinking other types e.g. juice, or even water, can propose or participate in toasts.
In prose, poetry and song lyrics, 'here's to...[someone or something]' can be used figuratively to compactly express support or admiration. An actual alcoholic toast may not be implied.
It is unusual to say 'Cheers to...' as the commencement of a toast, and I suspect that the words were used in that place, as so often in song lyrics, for reasons of rhyme, metre, etc.