battery connect to my circuit automatically when main power disconnected

[tpetar]

Hi tpetar,
you can avoid D1 since the rectified DC is more than 12v
regards ani

No D1 is there in case when there is no PSU power, why to waste battery power on PSU circuit resistance. ;-)

One ordinary linear voltage regulator can discharge small battery completely for some time.

 

[picgak]

Hi tpetar,
Ya that is correct
regards ani

 

[BradtheRad]

and your opinion about my final idea (final diagram)? is it good ? and don't have any problem?

Your second diagram is an improvement on your first (post #6). It is free of problems as far as it is a block diagram.

Now you are ready to add the other components. Such as the SPDT relay.

Some things can remain as blocks. Such as the primary supply at left. And your circuit at the right.

As soon as you figure out where to draw the rest of the components, it would be good to add them. The goal is to end up with a full working schematic.