I partially disagree with the two other answers (as of the time of this writing).
The Don't.
Let's use a slightly different example sentence to make the nuances clearer:
My classmates don't follow the rules.
This means that the classmates have a general habit of not following the rules. It's form of time-agnostic knowledge; it's possible that you're now attending another school and talking about ex-classmates.
The Won't.
My classmates won't follow the rules.
This suggests that there exists effort directed towards making the classmates follow rules. The phrasing gives an implication that there's an opposing force that's trying to behave your classmates.
Your example.
They don't let you smoke in here.
This is general; the speaker has probably deduced that from a no-smoking sign or similar.
They won't let you smoke in here.
This would imply that the speaker has probably actually tried to smoke once and they didn't let him. You might end up getting the implication that he tried to convince them ('oh, just this one cigarette'), which is the effort we mentioned in our conceptualization.
Note: this is a pretty small and nuanced difference; nobody will get confused if you use them interchangeably, but it does come quite naturally for native speakers.
Lastly: the In.
Simple:
It was getting crazy and hot in here.
This is localized; it was probably getting crazy in a room, hall, or some other enclosed 'cozy' place.
It was getting violent here.
This is more general and can refer to any type of place that is more likely abstractly-bordered-and-contained than having brick-and-mortar walls; think countries and nations, school campuses, streets, etc.
It’s too late to go shopping. The shops are open only until 5:30. They will be closed by now.
Yes, closed here is employed as an adjective. You are correct in understanding it to designate a state rather than an event.
And it is true that the expression by TIME is used with events rather than states—as your source says, it says that something ‘happens’ (an event) rather than ‘continues’ (a state).
HOWEVER: The expression by TIME does not compel you to employ an ‘eventive’ predicate or forbid you to use a ‘stative’ predicate. In fact, the compulsion works in the opposite direction: when you use by TIME, you compel your hearer to understand the predicate in an eventive sense. With by TIME the hearer interprets a stative predicate as the result of a change of state: something happened before TIME to bring about the state you describe.
Here are examples of by TIME with three stative verbs, know, own, be:
By April he knew that the operation was a failure. ... implies that he did not know this earlier, but at some time before April he learned that the operation was a failure
By 1973 he owned 26 newspapers. ... implies that he did not own so many newspapers earlier, but at some time before 1973 he acquired 26 newspapers
By next week you will be in Toronto. ... implies that you are not in Toronto now, but at some time before next week you will go to Toronto
In the same way, The shops will be closed by now implies that earlier the shops were open, but at some time before now the shops were closed. Since it is explicitly stated that the shops are open until 5:30, we understand that this sentence must have been uttered at some time after 5:30.
The word will may have caused you some confusion. This will does not designate some time in the future; it expresses a certain inference in the present. (Linguists call this ‘epistemic’ will.) Your last sentence may be paraphrased
It is certain that they are closed by now.
Best Answer
The usual phrase for the weekdays excluding the weekend is "during the work week" or just "during the week", not "in the week". "In the week" could mean all the days of the week, as for example in,
"There are seven days in the week."
Another way to refer to those days is as "weekday" or "weekdays":
Merriam-Webster "weekday"
"any day of the week except Sunday, or now usually except Saturday and Sunday"
For "during the week" you can say "on weekdays". That will be understood to exclude the weekend.
There are several idiomatic phrases used with the weekend:
on the weekend
at the weekend
during the weekend
over the weekend
The larger number of phrases for that time may be because the weekend is a special part of the week, and is often the focus of attention.
I think "grammar" refers to patterns of use that are general over a lot of expressions. I don't think these are grammar differences, just customary expressions.