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
- 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
- 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
- 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.
If anyone calls, tell him I am busy.
If anyone should call, tell him I am busy.
Now what is the difference between this two?
The first one is a normal conditional sentence, while the second one suggests that the event of calling is unlikely.
Notes from Practical English Usage by Michael Swan -
Should anyone call, tell him I am busy.
We can re-write this sentence as the following -
If anyone should call, tell him I am busy.
Note in the previous case Should anyone call...., we don't use calls.
Please visit this link for more information and examples of should used at the beginning of the sentence with if dropped, as you quoted in your question.
N.B Pam Peters in Cambridge Guide to English Usage suggests that the usage of should in conditional sentence is becoming less often. Conditional uses of should with if included in sentence now sound rather lofty, but the inverted should at the beginning of the sentence with no if included in that clause is still a neat way of prefacing a condition.
Best Answer
#2 is the informal, conversational version.
#1 and #3 have no difference in meaning and are both more formal than #2 due to the use of "should".
See also: Should versus If.