GIVE ANSWERS - Español

Que le vaya bien stands for may that goes good for him.

I think It is used to wish a good trip is short or long, for example when you leave a family visit or when you travel to another country. Whoever tells you, is looking forward to something good in general.

This is a big question! I think it hasn't got a purpose, we simply speak like that. You could also use the full sentence: "Espero que le vaya bien". Apart from that, we use it, for example, when we give an order we have already given before. Imagine that your mother tells you to make your bed.. the first time she well tell you: "haz la cama", using an imperative, but if after an hour she returns to your room and you haven't made it yet.. she could get angry and tell you: " ¡que hagas la cama!". In this case, you may also complete the sentence telling: "te he dicho que hagas la cama". I hope to be helpful!!