JavaScript self-invoking functions [duplicate]

Question 1

They are exactly the same. There is no difference whatsoever between the two in terms of efficiency, output, or use. Using either one is a matter of preference.

Though there is a shorter variation of the two forms commonly used by JS minfiers. That is, logical NOT-ing the function expression and calling it:

!function() {
    console.log( x );
}();

Question 2

No difference. In fact, you need to use () only because plain...

function() { console.log('bar'); } ();

... won't be properly recognized by JS parser. As said in the ES5 standard:

Also, an ExpressionStatement cannot start with the function keyword because that might make it ambiguous with a FunctionDeclaration.

The alternative (to (...)) solution is augmenting this statement with some unary operator. Both...

+function() { console.log('bar'); } ();

... and ...

!function() { console.log('bar'); } ();

... will work.

Question 3

There's no difference between them. Both are immediately invoked function expressions. Some people like Douglas Crockford prefer the second method. Some prefer the first. Interestingly Crockford's JSLint doesn't allow the first method, so I assume that the second one is more common.

Oh, and if you use a function declaration instead of a function expression then you can call the function before it appears in the program. This is because declarations are hoisted in JavaScript:

greet(); // This will work

function greet() {
    alert("Merry Christmas!");
}

The same is not true for function expressions:

greet(); // This will not work

var greet = function greet() {
    alert("Merry Christmas!");
};

That's pretty much all you need to know for now.