Who invented $\vee$ and $\wedge$, $\forall$ and $\exists$? I can rather easily imagine that some mathematician/logician had the idea to symbolize "it E xists" by $\exists$ - a reversed E - and after that some other (imitative) mathematician/logician had the idea to symbolize "for A ll" by $\forall$ - a reversed A. Or vice versa. (Maybe it was one and the same person.)
What is hard (for me) to imagine is, how the one who invented $\forall$ could fail to consider the notations $\vee$ and $\wedge$ such that today $(\forall x \in X) P(x)$ must be spelled out $\bigwedge_{x\in X} P(x)$ instead of $\bigvee_{x\in X}P(x)$? (Or vice versa.)
Since I know that this is not a real question, let me ask it like this: Where can I find more about this observation?
 A: The four types of propositions used in the classical Greek syllogisms were called A, E, I, O.  Statements of type A were "All p are q".  Statement of type E were "Some p are q".  So of course a millennium later, mathematicians (who had a classical education) used A and E for these quantifiers, then later turned them upside down to avoid confusion with letters used for other things.   
By the way: I and O were "All p are not q" = "No p are q" and "Some p are not q"="Not all p are q", but I don't remember which is I and which is O.
A: I've misplaced my copy of it, but I recall S. C. Kleene in his Mathematical Logic noting that "v" came as an abbreviation of "vel".  In Latin "vel" is one of the words which commonly gets translated to the English word "or", and at least people believed that the Latin word "vel"  comes closer to alternation (or equivalently, inclusive disjunction) than any of the other words which commonly get translated as "or".  Since Russell read Peano, and Peano's book on arithmetic got written in Latin, it does seem at least plausible that Russell first used "v" for alternation, as Bill's reference states.
That "∀" has to get interpreted by "⋀" as you correctly state in at least some cases (though not always), may seem strange at first, I agree.  But, one way to think of things here comes as to have the truth set as linearly ordered.  When you do this with "0" as the least truth value, and "1" as the greatest truth value, "⋀" most closely corresponds to, if not in fact is, the infimum, while "v" most closely corresponds to the supremum.  Both "infimum" and "supremum", at least according to my intuition of them, involve notions just as strange if you don't look at them carefully.  
A: My understanding of the quantifier symbols $\bigvee$ ("there exists") and $\bigwedge$ ("for all") was that they were supposed to be large versions of $\vee$ ("or") and $\wedge$ ("and"). Then $\bigvee_{x\in X}Fx$ would mean $Fx_1\vee Fx_2\vee Fx_3\vee\dots$ whereas $\bigwedge_{x\in X}Fx$ would mean $Fx_1\wedge Fx_2\wedge Fx_3\wedge\dots$
This is similar to the notation $\bigcup_{x\in X}S_x$ for $S_{x_1}\cup S_{x_2}\cup S_{x_3}\cup\dots$ and $\bigcap_{x\in X}S_x$ for $S_{x_1}\cap S_{x_2}\cap S_{x_3}\cap\dots$
I don't see that these symbols "fail".  I can see that $\forall$ could be confused for $\bigvee$, and that would be bad since $\forall$ means the same as $\bigwedge$. However, I don't see that as being a condemnation of one over the other, and there would be no confusion if only one were being used at a time.
A: See Earliest Uses of Symbols of Set Theory and Logic for this and much more.
A: 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.
