Oh, I dropped the link when I was citing that entry:
でもを英語に訳すと。英訳。1〔しかし〕でも大して役には立ちませんよIt won't be of much use, though.でももう遅過ぎるBut it's too late.彼は責任感がないんだ.でも両親の晩年の世話はよくしたHe has no sense of responsibility. Nevertheless, he did take good care of his parents in their o... - 80万項目以上収録、例文・コロケーションが豊富な無料英和和英辞典。
I can see from a dictionary that なりmeans "or something" but not too sure what なりと means here.
It also means "or something" here. That's a dictionary entry -- it's just being given as the definition of でも. If you're not familiar with (and it's much less common than でも so there's no reason you would be) then don't worry about it.
So this means "tomorrow or some day", I guess.
Yes.
明日にでも行きましょうかね Shall we go tomorrow (or sometime)?
待っている間よかったらその雑誌でも読んでいなさい Why don't you read that magazine or something while we wait.
I believe this is literally 読んでいる + なさい, a progressive form of 読む even though the translation is not done accordingly but perhaps naturally.
Yes.
"なさい" is used, for example, when a mother is scolding her child or when a teacher wants a delinquent student to pay attention. Why would one need to use「なさい」 being a special honorific conjugation of 「する」for parent to children and teacher to students?
なさい isn't a conjugation of する, but rather a conjugation of an alternative honorific word なさる. Not quite the same thing.
Using the honorific in an imperative form softens imperative into a request, I think? (Even though it's quite a stern request and nearly imperative). It's also possible なする has shifted in meaning, I'm not quite sure.
It's a bit odd, but there are a lot of bits of Japanese where an expression was formed at a time when the language was used differently, and then that expression was carried intact into modern Japanese where it doesn't quite match the regular rules. I believe なさい is one of those, and I don't normally think of it as being a conjugation of なさる so much as a grammar derived from なさる.
I was expecting 世界に in the sentence because I thought it meant "in the world".
It does in some contexts. Unfortunately, Japanese particles and English prepositions don't always line up neatly. It does take some getting used to.