Learn English – “Fetch some water in a quiver” or “Get some water in a quiver”

"Any question" places a strict limit on the number of questions allowable to exactly one. For example, there was exactly one question as to who wore the pants. However, where the number of questions has not been determined, or is unrestricted, then the plural should be used.

Is there any question that I am correct? I don' think so. (The only question might be "are you correct".) However, any questions you have should be added to the comments below. (Questions might be "are you serious?", "what authority do you cite?", "why is your speellling so bad?" and so forth.)

In my (UK) idiolect "have a rest" and "get some rest" are idiomatic, not the two phrases you give.

I find a slight difference in meaning. To me, "have a rest" is neutral: I am going to rest, with no implication about how much I need it.

"Get some rest" implies that I have a particular need for rest: either I have been short of rest recently, or some major activity is expected so that I need to be well-rested before it, or there is very little time available for resting, so I will avail myself of it.