Learn English – difference between “should not have done something” and “needn’t have done something”

To answer your first question 'must' is possible in the above example but the meaning will be different than i suppose you have in your mind

When we use 'should' we think what is right/moral/decent thing to do at the time.

When you say 'They should have called the police.' - (Here you know it for sure that police have not been called)

But when you say 'They must have called the police.' (Here you are almost instinctively sure that the police had been called after you have anaylzed the situation well, but officially you don't know whether they called the police or not)

See below how 'should' and 'must' function in your examples

They should have called the police. (It is your opinion)

They must have called the police. (It is your speculation)

For Example

1. There has been a burglary in one of the houses in your neighborhood. Now, any random family would call the police in this situation. So it is extremely easy for you to speculate that 'They must have called the police' - because that was the sensible and normal thing to do after the burglary.

But when you know that they didn't call the police in this situation then you might express your surprise in the following sentence

1. I am surprised that they didn't call the police after the burglary. They should have called the police and informed them about it. (Must is not possible in this example)

Another example

Suppse you are telling your friend the following

1. If you were having such a hard time at school, then you should have told me. (meaning that you might have been able to help your friend out)

Here 'must' is not possible - because you can't compel your friend to share things with you. Sharing is not compulsion. So you can't say --

You must share your problems / feelings with others.

But you say --

You should share your problems / feelings with others.

'Must' in one of its meanings implies compulsion, obligation etc.

To answer your second question -

You should read his new book. (Sounds less convicing than 'must' but it is still a suggestion)

Here 'should' works as a suggestion But You must read his new book. (sounds more convicing)

If there is any book or movie that you have liked very very much then you use 'must' not should. 'Must' will work as 'strongly recommended'

So it should be

You must read his new book. It's amazing.

No, "should" is not generally interchangeable with "would". The easiest rule of thumb is that when a speaker uses "should" she is prepared to explain why, and when a speakers uses "would" she is prepared to explain why not. Here are some examples:

Muskie should have won by a huge margin [because he is much better than the competition].

Muskie should win tomorrow [because he is much better than the competition].

You should have heard by now that I'm OK [because I saw the doctor talking to you].

You really should have started that paper more than 8 hours before it was due [because it's very difficult to write a quality paper in less than 8 hours].

With "should", the speaker always has a reason why something did/will occur. If the speaker's reason [in brackets] isn't explicitly stated, it is still implied. Now consider "would":

Muskie would have won by a huge margin [if he didn't blow his engine].

You would have heard by now that I'm OK [but you didn't buy me a cell phone, so I couldn't call you].

I would have started that paper earlier [if I wasn't so busy with all my other homework].

With "would", the speaker always has a reason why not - why something did not occur. The speaker is more likely to explicitly state her reason [in brackets] with "would". If we are using a future tense, the why not rule of thumb becomes awkward but still workable:

I think she would like this as a gift [if we decide to buy it for her].

In sentences like this, everyone understands that it is hypothetical, so the speaker would rarely actually say the reason in brackets [if this hypothetical situation ever arose]. (See what I did there!)

One final note, which makes this kind of tricky, is that you can still use "should" even when you state a why not reason as long as a why reason is still stated or implied:

Muskie should have won if he didn't blow his engine.

Actually means:

Muskie should have won if he didn't blow his engine [because he is much better than the competition].

So in sentences like this, "would" and "should" are almost interchangeable. Just remember that "should" means the speaker knows why and "would" means the speaker knows why not. If the speaker happens to know both, then she can choose "should" or "would" almost equivalently.