Returning const reference to local variable from a function

Q1: Yes, this is a problem, see answer to Q2.

Q2: 1 and 2 are undefined as they refer to local variables on the stack of getA1 and getA2. Those variables go out of scope and are no longer available and worse can be overwritten as the stack is constantly changing. getA3 works since a copy of the return value is created and returned to the caller.

Q3: No such guarantee exists to see answer to Q2.

1. Is getA1() implementation correct ? I feel it is incorrect as it is returning address of local variable or temporary.

The only version of getAx() that is correct in your program is getA3(). Both of the others have undefined behaviour no matter how you use them later.

2. Which of the statements in main ( 1,2,3) will lead to undefined behavior ?

In one sense none of them. For 1 and 2 the undefined behaviour is as a result of the bodies of the functions. For the last line, newA3 should be a compile error as you cannot bind a temporary to a non const reference.

3. In const A& newA1 = getA1(); does standard guarantees that temporary bound by a const reference will not be destroyed until the reference goes out of scope?

No. The following is an example of that:

A const & newConstA3 = getA3 ();

Here, getA3() returns a temporary and the lifetime of that temporary is now bound to the object newConstA3. In other words the temporary will exist until newConstA3 goes out of scope.