He may have noticed 1⃣️ that she's not feeling very well / 2⃣️ that she was not feeling very well / 3⃣️ that she has not been feeling very well/ 4⃣️ that she had not been feeling very well (Are all of them correct? Would it be possible for you to explain the difference between them to me? )

> Are all of them correct?
I can’t answer this because whether or not they’re correct depends on what you want to say (the context), and I don’t know the context. I can think of contexts in which I might use the first three, so I can say they’re grammatically possible, but the 4th doesn’t seem possible to me.

> Would it be possible for you to explain the difference between them to me?
Doing so would require me to describe contexts in which each variant would be used. Sorry, but I don’t want to spend that much time on this.
¯\_(ツ)_/¯

You might like the materials on this website: https://www.englishpage.com/modals/modalintro.html

Note that there’s a separate page for each modal, for example “might”: https://www.englishpage.com/modals/might.html

(If it is a missed opportunity, does it mean that I can't replace COULD with MIGHT or MAY? )

In my opinion, you could replace it with “might” but not “may.” But these grammatical “rules” vary a lot from region to region: what sounds natural to me might sound unnatural to someone from somewhere else and vice-versa.

You should have informed me that there's / there would be a meeting today.

I would tend to say “there would be” in this context, but it’s possible that “there’s” would sound natural to some native English speakers.

I ought to have known that this relationship will/ wouldn't last long.