Questions about たり and the たりする construction.

Most sources seem to describe たりする as a set construction, and that this is used to make a non-exhaustive list of activities. I have two questions:

1. The following example is found on this page:

休みの日は水曜日だったり、日曜日だったりです。We are closed on Wednesdays and Sundays.

How should this sentence be understood in the context of a non-exhaustive list? Unless I'm misunderstanding something here, it seems like saying "We are closed on Wednesdays and Sundays" doesn't leave much room for any other possibilities. Or does it mean they may be closed on other days as well (in which case, surely it is a pointless statement then...?)?

2. Is there a difference between putting です or します at the end of the sentence?

1. Yes. I take it to mean that Wednesday and Sundays are their normal days off. But occasionally they might be closed on other days such as New Years holiday or whatever.
2. I'm not sure. Perhaps when the copula is used with nouns like this, the correct form is です. And when verbs are used as we are typically taught then it's します. Let's see what the experts say. I can't recall ever using this form with nouns. So maybe I can say something like, 日本に行って食べたいのは天ぷらだったり、焼き肉だったりです。It sounds odd to me but it might be ok grammatically.

Interestingly a native speaker thought your example meant
日曜日のときもあるし水曜日の時もある。水曜日と日曜日ではないんだろうな、でもたまに他の曜日もあるのかも、って思う
which is different from the given translation. But this interpretation might be based on cultural knowledge. That is, it would be out of the norm for a shop to close two days a week. But the assumption that it could be other days besides Sunday and Wednesday was aligned with what I thought.

↑ Yes this is what I thought as well.

The day when the shop is closed is typically Wednesday, but sometimes we are closed Sunday. It depends on the week.

します , doesn't work at the end of this sentence. I usually get into trouble when I try to explain why... but it feels to me like a question of volition. There is no "subject" who is doing the closing, so します doesn't work. です is more like the passive voice in this sentence, and just indicates "the shop is closed" rather than "I am closing the shop" or "We are closing the shop".

Agreed. It's "or", not "and", there.

～たり…たりする is not always "a non-exhaustive list". It can be an exhaustive list. For example, 行ったり行かなかったりする is legitimate, and this is an exhaustive list since there is no other option than "to go" and "not to go". In other words, they might be closed only Wednesday or Sunday.

This expression works as an idiom, and する can be used also for non-action nouns.
examples in a corpus
その融資責任者が現役の頭取だったり、院政をふるう会長や相談役だったりするために
その世界に入ると、結局はお金儲けだったり、妥協の世界だったりすることが分かってくるの。
こういった行動のうちどれかが自然だったり不自然だったりするわけではなく
それは、素晴らしい選手だったり、鮮やかなプレイだったりするが
そのきっかけは、なにかの香りだったり、音やイメージだったりする。

Thus, there is no problem with 休みの日は水曜日だったり、日曜日だったりします。. There is no difference in meaning or nuance here.