1.

“En” is found in an idiomatic turn here and does not mean anything (not any more at least). This construction is “s’en vouloir” which takes different forms according to the subject.

• First person singular     Je m’en veux
• Second                         Tu t’en veux
• Third                             Il s’en veut
• First person plural:       Nous nous en voulons
• Second                         Vous vous en voulez
• Third                             Ils s’en veulent

The translation provided by the machine is wrong. In English this means “to blame oneself”; so the sentence would read as follows instead of “He does not want to ask himself all these questions about this boy.”.

• He is blaming himself for asking all those questions about this boy.

2.

Here, things are different; “en” does mean something; it’s a pronoun and its antecedent is rather difficult to make out. From the TLFi we get the following possibilities for the antecedent.

En tant que pronom, en se construit avec un antécédent de nature substantive, qu’il s’agisse

• d’un subst. proprement dit ou

• d’un pronom qui le représente, ou

• d’un subst. inclus dans une loc. adv., ou enfin

• d’une prop. reprise en tant qu’entité globale après nominalisation implicite par en.

The fourth case is what’s applicable here. The clause (proposition) is what precedes, that is “Afrique expliqua. ‘Il faut laisser les plus jeunes en arrière’.”; the nominalisation (same word in French) consists in thinking about how to transform what this sentence says into a noun; there is no unique way of thinking about it as a noun and in reading, once you are used to French, you never do that or rather you do it abstractly and very fast in your mind. However, in order to understand the process theoretically, this has to be done. Here then are possible nominalisations.

• L’explication qu’il faut laisser les plus jeunes derrière
• L’idée qu’il faut laisser les plus jeunes derrière
• Le dire d’Afrique qu’il faut laisser les plus jeunes derrière
• Le fait qu’il faut laisser les plus jeunes derrière

You will notice that you can use all those sentences as subject in a sentence, for instance by adding “n’est pas à prendre au sérieux.”; this means that they have the value of a noun in grammar as mainly the subject in a sentence is a noun.
Therefore “en” stands for the expression that what this noun says is the cause for the king of the goats’ pulling off three beard hairs; the cause is rendered by the preposition “de” which we add in the replacement. This question of cause being rendered by “de” is contained in another line of the introduction to the entry in the TLFi (above reference).

À l’intérieur de la proposition où il est placé, « en » remplit auprès des termes de cette proposition toutes les fonctions assumées par « de », soit dans ses emplois de préposition, soit dans ses emplois d’article indéfini ou partitif (de, du). Lorsqu’il représente un antécédent substantif proprement dit, il peut être lui-même déterminé dans certaines limites.

Of all those fonctions it is a question of in this explanation three are essential: origin, cause, means. Here, the cause is the relevant fonction.

“Le roi des Chèvres s’en arracha trois poils de barbe.” is then equivalent to what follows.

• De cette explication que les jeunes devaient être laissés derrière le roi des Chèvres s’ arracha trois poils de barbe.
  (Because of this explanation that the young had to be left behind, the king of the goats pulled off three hairs from his beard.)

“De” is used for generalising; however in this particular case a better prepositional form would be the prepositional locution “en raison de”.

• En raison de cette explication que les jeunes devaient être laissés derrière le roi des Chèvres s’ arracha trois poils de barbe.

So as to consolidate the idea we might consider some examples regarding the fonctions “origin” and “means” as embodied in nominalised clauses.

• (origin) Il y avait des carcasses aux os desquelles étaient encore accrochés des lambeaux de peau tâchés de sang et il en déduisit que des animaux féroces peuplaient la contrée.
  (It seems to me that the idea involved is “origin”; the source of the deduction is the reckoning that there is dry blood on the skin; however someone might argue that what is really implied is “cause”; I would say then that the cause or reason for the deduction is not truly that but it would rather be the fact that for blood to be found on the skin, it had to result from a wound.)

• (means) Il remarqua que l’avocat de la défense avait négligé plusieurs aspects qui rendait sa plaidoirie vulnérable et le procureur en étaya un réquisitoire visant à montrer le but dissimulateur de la défense.
  (The particularity in the approach of the defense lawyer is used by the prosecutor to achieve his aim of showing culpability; this particularity in the approach of the defense lawyer is therefore a means.)