Question: If I'm asking "How are you?" to a singular person in a formal way, why to I say "Как Ваши дела" instead of "Как Ваш дела"? Does "Как Ваш дела" mean anything?

Answer: 
We use *Ваши* because it is for the plural *дела*. The whole phrase is in the Nominative case, just like, for example, мои друзья (мои друзья здесь), твои книги (твои книги интересные), **Ваши** столы (Ваши столы красивые) etc.

When we ask somebody about how something/someone is, we use the **Nominative**:

> 
> Как ваши друзья? - Хорошо.
> 
> 
> Как твой проект? - Плохо. BUT Как *твои* *проекты*? - Плохо.
> 
> 
> Как Ваши дела? - Отлично.
> 
> 
> 

"Как Ваш дела" is ungrammatical.
> 
> Does "Как Ваш дела" mean anything?
> 
> 
> 

No, it's a mistake. The pronoun should be in the plural because it refers to the plural noun дела. **Ваши** is a polite form and it can be used addressing one person and a group as well. If you know a person well you can say 

> 
> Как твои дела?
> 
> 
> 

There are also informal greetings avoiding the addressee (we don't say possessive pronouns as often as they are used in English)

> 
> Как дела? Как жизнь? Как оно ничего?(joking) Что новенького?
> 
> 
>