I suspect the difference in the first case may not be a difference in literal meaning as much as a difference in how English vs Japanese speakers tend to view and express certain situations, and may be a matter of context. The Japanese sentence is saying that as a general situation, it is always closed on Monday nights. However, if the surrounding events that are being described are things that happened in the past, it is common for an English speaker to also phrase that sort of situation in a past tense as well, even if it may also be true in the present and in general, for example:
I wanted to go to my favorite restaurant, but on Monday nights it was closed, so I went to the place down the street instead.
This doesn't mean it isn't also closed on Monday nights now too (it probably is, because it's a general condition), and indeed you probably could phrase it in the present tense too, but it's just that (at least to many people) it sounds better in English when expressed with matching tenses to all of the surrounding text instead. (but this is often not as strong a factor in Japanese)
For the second passage, I think it's important to understand that the する in that sentence is essentially part of a subclause modifying なんて, so it is more a descriptive qualifier than referring to an actual occurrence.
In this sort of situation where a verb is modifying something that comes after it, it is sometimes useful to view the non-past (する) form as somewhat similar to the gerund (-ing) form in English, that is:
彼があんなことをするなんて信じられない -- "Something like (なんて) him doing that sort of thing (彼があんなことをする) is unbelievable (信じられない)"