Here are your answers:
1. Pierre et Laurent n'ont pas de sœur.
Pierre and Laurent are two people, which makes this subject a 3rd person plural, "they", or in French, "Ils". The conjugation of the verb avoir goes as follows:
J'ai
Tu as
Il/Elle a
Nous avons
Vous avez
Ils/Elles ont
Therefore, we need the ont to conjugate the verb correctly in this sentence.
2. Ton cousin et toi avez 15 ans.
In this sentence, "ton cousin" = "your cousin" and "toi" = "you", means that this is a 2nd person plural, "you" or "vous" in French. It is the plural because we also have two people, your cousin AND you. And as shown before, the conjugation is this one:
J'ai
Tu as
Il/Elle a
Nous avons
Vous avez
Ils/Elles ont
Vous avez is the correct option.
