A few things I dont understand

Question

In the sentence "qui vient d'accueillir son premier animal familier" - Why are we using "son"? I've read the lesson still don't understand. Is it because of it being used generally?

In the sentence - "Je dirais que le plus important est d'apprendre à vivre ensemble" why is there no "chose" involved to mean "the most important thing"?

And in that same sentence, why is it that "De" is used to express "TO learn"? why not "à"?

Also in the sentence "ce soit bon pour un animal de rester enfermé" is the "De" required because of "être"?

And lastly - "la plus grande preuve d'amour que vous puissiez lui donner" why did this sentence get knocked into the subjunctive?

Apologies for all these questions but this exercise really got me confused!

Accepted Answer

I'll go in order:
1) son is used in the meaning of an impersonal "one's". And in that instance, French resorts to the male form. It's just as logical or illogical as "their" in English. ;)
2) Les plus important -- in that phrase, the adjective important is used in lieu of a noun. Literally: the most important (thing/issue/fact) is... This doesn't work in English, where you can't really omit the noun.
3) de after être means "to". There may be a fancy grammatical term for this, but I just simply suggest you internalize this. 
C'est important de faire ses devoirs. -- It is important to do one's homework.
4) Ce soit bon pour un animal de rester enfermé. Yes, it's the same kind of de then in the previous question.
5) The sentence is in the subjunctive because of the superlative. The superlative (being considered as engendering some speculative element) often is used in conjunction with the sujunctive. Here is more on this: 
superlative-subjunctive/  -  Subjonctif-with-sentences-using-superlatives

Answer

Thank you very much for your help!