Is this diagram possible ?Using only one transformer to doubble the voltage and Amp .?

Yes, you will get 120 volts out, but only 5 amps. You cannot get free power.

And the 120 volts will NOT be suited for domestic use, as it is balanced around ground, with two hot lines of 60 volts each. You can fix that by removing the ground shown and grounding L2.

And you would have better results, less heating and less cost, if you had one winding for primary and one for secondary.

The current rating of a winding is a capacity limit for that winding. It is not the current it uses or provides. If you should load the secondary to 20 Amps, that would attempt to draw 40 Amps from the primary resulting in a failure / fire. The output power, the product of the output voltage and current is always limited to the efficiency (<1) times the input power, the product of the input voltage and current. The efficiency of a transformer can be over 90%, but never more than 100%.

If the voltage is doubled, the current must be half since V*I in = V*I out (ignoring losses). If there were free power or free energy, our planet would be a very different place.

This is the most stupid way to imagine getting more power from nowhere without knowing the basic structure of transformer and AC power source. Here are the mistakes....

[1] As Primary section consumes power not more than 600VA, how could it output 2400VA.

[2] Neutral links to main power source return terminal , secondary winding is isolated from primary while the transformer was made. Hooking neutral to secondary winding does no affect to it.

[3] Parallel transformer windings is bad practice because their voltages ever equal the same, result overheat to transformer.

You will get 120 VAC out of it, but if you try to draw 20 amps from the secondary, the primary will draw 40 amps. A transformer doesn't give you free power.