How an 'if (A && B)' statement is evaluated?

You are asking about the && operator, not the if statement.

&& short-circuits, meaning that if while working it meets a condition which results in only one answer, it will stop working and use that answer.

So, 0 && x will execute 0, then terminate because there is no way for the expression to evaluate non-zero regardless of what is the second parameter to &&.

In C and C++, the && and || operators "short-circuit". That means that they only evaluate a parameter if required. If the first parameter to && is false, or the first to || is true, the rest will not be evaluated.

The code you posted is safe, though I question why you'd include an empty else block.

Yes, it is called Short-circuit Evaluation.

If the validity of the boolean statement can be assured after part of the statement, the rest is not evaluated.

This is very important when some of the statements have side-effects.