1- Why is it important for Lenina to publicly prove her unfaithfulness to Henry?

The unfaithfulness to Lenina is note very important in the book, because in the book that was normal,all the people have por than one couple, so we can say that in that world de unfaithflness doesn't exist

                                                                                                

2- Is it natural to be in a couple and raise a family in the Brave new World? Why/why not?

It's not natural, because the social rules at that time say that this is not correct, In the contra part they thought that the human being should have many couples and that should not be enslaved by way of a only couple. This is reflected in the chapter 3 page 35: "Their world (the past) didn't allow them to take things easily, didn't allow them to be sane, virtuous, happy." That is why this question is totally related to the unfaithfulness of the world of brave new world in which it is assumed that someone can be happy only if it is free to be with anyone, in wherever they want and however they want.

3- What is the meaning of "pneumatic" when it is used to describe Lenina?

This description can be metaphorical. It seems that he wants to mean that she's busty, curvy, and all-around sexy.

4- What is “Soma” and why do people use it?

its a designer drug with no side effects can cure feelings of sadness and who use every time they want a vacation or experience negative emotions and want to escape reality and is shown according to chapter 4 page 52: "you do look glum! What do you need is a gramme of soma. Diving into his right-hand trouser-pocket.Benito produced a phial. One cubic centimeter cures ten gloomy ... but, I say

5- Was Bernard a tall or a short man? How did this affect his job? Please justify your answer by quoting from chapter 5.

Bernard was a short man. In his job he was affected because he feel "looked" by the society because was different that the others. The mockery make that Bernard feel like a outsider because his shorter than the others.