Could have, Should have, Would have, Must have, Might have - Time Adverbs

Question

When talking about past ability or possibility, we use could have or might have.

When talking about past obligation or suggestion, we use should have.

When talking about past strong guess, we use must have.

When talking about past intention, we use would have.

I know the topic above has been discussed thousands of times in this forum, but nobody has ever asked if they have any limitation when it comes to time adverbs. So, I decided to ask the below question. By the way, I guess that since they are used to describe and portray things in the past, their time adverbs are just like simple tense's.

Question:

Can they (would have, could have, might have, should have, must have) be used with past time adverbs: yesterday, last year, last week, by May 5, at 5 pm, by 10 am.....etc?

Example provided to make discussion easier:

1. He could have played with his friends online at 5 yesterday. (which I am not sure about, so I take a guess)

2. He should have studied smart and hard last year. Courses last year were important for his future career. (I don't know if he studied hard and smart last year. I just want to convey the idea "he was supposed to study hard and smart")

3. Students must have gone to class instead of taking class online in the 90s.

4. The patient must have taken the medication at 5 last night. That medication is important part of the treatment. (the patient had to take that medication at 5 last night.)

5. In high school, with the internet, I would have got a better result on the admission test.

Answer 1

Yes, you can use these sorts of phrases with time adverbs just fine.

However "must have", in this case, basically describes a strong guess or belief. It does not mean there was a requirement or need.

...must have taken the medication...

basically means:

...almost definitely took the medication...

It doesn't mean:

...needed to take the medication...

or:

...was required to take the medication...