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.
shoot & shot are film/movie & professional photographic terms.
shoot describes the 'event' at which film stock is used to make the movie/photographs.
The shoot is a general term for the entire occasion, at which there may be several hundred people, all doing different tasks that make up the event; from catering, locations & logistics, transport, carpenters & riggers, lighting specialists, sound recordists, cameramen & grips [camera movers], production crew, actors, director … all are on the same 'shoot'.
Stills & movie would be differentiated as
photo shoot / stills shoot or
film shoot / movie shoot.
'stills' is the movie term for non-moving pictures.
A stills photographer would call them shots or photographs, as there is no 'moving' alternative to cause confusion.
A shot is either
- The specific way the camera is lined up &/or moved, re-focussed etc., to point at the actors or scene, in order to film that one small section of the action, or
- for stills photography, either the above, or simply any one single photograph - whether it required an entire film crew to take it or not.
An aside… this is where we get the term "Who is calling the shots?"
The answer is - the Director.
Best Answer
"To have no trouble doing something" means to find it easy or convenient.
"To have no problem doing something" means not to object to it.
In perhaps less common cases, the second one can also be used in place of the first.