In this contexts, would functions as the past tense of will.
To take the second example first,
Her mother didn't let her go to the party.
is stating a fact that happens to be in the past, but from no particular temporal focus.
Her mother wouldn't let her go to the party.
is setting the temporal focus back at that time, at the time when "her mother won't let her go to the party".
There is no objective difference between these two, and not much practical difference; but it sets the narrative back at that time, and suggests that there was a continuing process - maybe she asked several times.
The first example is similar, except that I find the would strange here, unless you are reading a biography, or a history of his works. Again, the would sets the temporal focus back to the time when he published, so that the criticism is in the future.
Your third example is quite different. Often both modals are possible, and objectively synonymous. But they exhibit different degrees of tentativeness, and hence of politeness.
Would you help me.
is literally "Are you willing to help me" (though it is rare that anybody would actually say that). It can vary from a polite request to a peremptory command, depending on the tone of voice (though it still has the surface appearance of politeness even in the latter case).
Could you help me.
is literally "Are you able to help me", but tends to be interpreted as "Is it possible you will help me" - more tentative and less likely to be peremptory.