Some crazy question regarding atomic theory and electronics theory! please help...?

'we know that current is nothing but flow of electrons,then when joining this with atom theory, then atom would get unstable, when electrons will flow.

It's a flow of electrons. When one leaves another flows in. The material the current is flowing through doesn't lose or gain any electrons.

Also, most elements are more stable when they lose or gain electrons and become ions. Elemental sodium is unstable. We only find it in nature as a positively charged ion(Na+). This is true of all the A1 metals(first column of the periodic table). The electrons don't stabilize the nucleus. At high temperatures atoms can exist in a state where they have no electrons at all. An alpha particle is a naked nucleus of helium. Alpha particles are emitted by several radioactive isotopes.

In a metal, some of the outer atomic electrons are able to escape from their atoms (this leaves behind positive metal ions).

The electrons that have escaped are called conduction electrons (or delocalised electrons). They are able to move around between the positive metal ions.

If you connect a piece of wire to a battery, conduction electrons can then flow through the wire. (Some electrons leave from one end of the wire but are replaced by electrons entering the other end of the wire.)

The short video in the link shows this.

the main problem appears to be a failure to understand that charge is not atom-specific, but is distance-related. The total balance of forces distributes over a wider area, so there is no real energy lack at a specific location that is of sufficient magnitude to cause instability.

There most certainly is a small disruption of the energy balance, which is created by the electromotive force (otherwise there would be no motion). The disruption is diffused rather than localized.