Translation:This hospital is closed on Monday.
I really hate this "closed" vs "shut" thing. I keep typing "shut" on pretty much every question that has the word "closed" in it. Even though Duo tells me off every time, I keep typing "shut" without realising and then getting marked wrong. ><;
I still don't know whether "shut" is even correct English. But then why do I nearly always instictively type it this way if it's not? ^^;
I can't say I've ever heard the phrase "shut shop", though it absolutely makes sense.
The closest thing I can attest to is a simple phrase of 'It's time to close up shop' - but again, it seems to avoid the word 'shut'.
The only other thing that comes to mind is: "Time to shut it down" I've heard used at bars around closing time.
The British 'shut' struggle is real. Hopefully they'll do more to accommodate that in the future.
The word shut, in the USA, is usually referring to windows or doors. For businesses or shops, we use the words open or closed. Examples... "The store is closed", "The store is open". Or it can be used as a verb. "I closed last night", which means, I worked last night until close and helped close the shop for business.
It's contrasting the hospital with something else. The first「は」in a sentence marks the topic, any following「は」mark a contrast. In English, we'd typically achieve the same effect by putting extra force into the word when speaking.
"Regarding Monday, this hospital (as opposed to other hospitals) will be closed."
Note that「は」is still a particle here, so it is pronounced "wa", not "ha".
に particle often implies both a time and a place. By saying 月曜日は, you're speaking of "As for Monday...", implying that the following occurs on Monday (time) without specifying a place, since the hospital (place) is the subject of the sentence in this case that is being closed on Monday (topic).
～ています (~te imasu) is usually best translated with the English present progressive (is ~ing / are ~ing) because it is reflecting what something is currently doing. But the Japanese can also be used to tell about a continuous state of being. The hospital is in a continuous state of being closed on Mondays, which in English is best translated as "the hospital is closed on Mondays".
I think the Japanese way of thinking might be different from ours.
When describing a place that is closed, Japanese uses the -te form.
Getsuyoubi wa kono byouin wa shimatte imasu.
The hospital is in a continuous state of being closed on Monday.
Examples from Tanos:
あいにく店は閉まっていた。 Unfortunately, the store was closed.
Ainiku mise wa shimatte ita.
イギリスでは、日曜日にお店が閉まっていますか。 Are the stores closed on Sunday in England?
Igirisu de wa, nichiyoubi ni omise ga shimatte imasu ka?
このデパートは今日は閉まっている。 This department store is closed today.
Kono depaato wa kyou wa shimatte iru.
You use the -masu form a little differently.
このレストランは何時に閉まりますか。 What time does this restaurant close?
Kono resutoran wa nanji ni shimarimasu ka?
ジョンの言うことには、銀行は午後３時に閉まる。 According to John, the bank closes at 3 p.m.
Jon no iu koto ni wa, ginkou wa gogo 3ji ni shimaru.
閉まります (shimarimasu) is used for the exact instant that something closes.
3時に閉まります (3ji ni shimarimasu). It closes at 3. From 3:01, the store is closed, it is 閉まっています (shimatte imasu).