That's a nice question, but you misunderstood the creation of the universal quantifier "all" and "there exists". It appears to be derived from the letter A, and I guess it is, but it didn't emerge that way. The first one to introduce quantifiers the way we know today was Gottlob Frege, who was a german mathematician, in the book Begriffsschrift. See the article about his book on wikipedia, it has the notation used for him. So, that clarifies your question about $\forall$ and $\exists$. In regard of "e" and "or", they are just Boolean connectives, introduced by George Boole in Investigation of the laws of thought. The use of "or" as $\vee$ it's just a convention, Quine explains it in his Mathematical logic, as just an abreviation of the latim word "vel". The use of "e" as $\wedge$ it's, again, a convention, many mathematicians in the analytic tradition use dots (.) instead of. Answering your last question. You're thinking about quantification in a wrong way, it's not just about "quantifying" (read Quine's ML), it's about signing, you use it just to show the variable place in a statement. Using Quine's example: suppose you want to say that every number is less than $0$, equal to $0$ or different from $0$, then you say "Whatever number you may select, it $<0$ $\vee$ it$=0$ $\vee$ it$>0$", or, "whatever number (it $<0$ $\vee$ it$=0$ $\vee$ it$>0$)". Now, for simplification, instead of using the last one, just say "$(x)$ number ($x>0 \vee x=0 \vee x<0)$". Mathematically, you just say $(x)(x \epsilon Number (x>0 \vee x=0 \vee x<0))$. So, $\bigwedge _{x\epsilon Number} P(x)$ it's just an abreviation of $(x)(x \epsilon Number (P(x)))$ but what if you wanted just to say $(x)(x=x)$ without specifying a class, like Number or $X$? You would had to introduce quantification in the notation, and it would get messy. I know my example doesn't clarify a lot, but the quantification business isn't as clear as everyone thinks, there are a lot of divergence between the professionals. Russell for example, in his Mathematical logic as based on the theory of types talks a lot about quantification, and you can see it's not a simple, it involves a lot philosophy. So, read Quine and Russell. Have a nice day.
P.S.: Consider this: $(x)(x \epsilon N .\supset. P(x))$, so, suppose we want to say that using the "and" quantifier, than it becomes $(x_1,..,x_n \epsilon N)(P(x_1) \wedge .. \wedge P(x))$ which is a lot more work, and still have to use quantification. Definitions are a way of simplification. But, read Russell (Principia and the article I mencioned) and Quine, quantification used in modern mathematical logic come from their works, see if the philosophical approach correspond to what we just did.