Why atoms do not repel each other when electrons are outside of nuclear. I think inverse square law of force doesn't allow atoms to come close and form molecules but in reality atoms come close and form molecules. How ?
Simply because there are other than columbic forces acting on it. Why electron "cloud" overlapping does reduce potential energy of a system cannot be simply stated from classical mechanics- you need quantum mechanical description. You cannot reduce hydrogen on van-der-Waals bond to coloumbic inverse-square law. Classically you may say that the nucleus of one atom does attract electron cloud of other atom, and electrons are not "evenly outside in all directions" for any bonded atom. In fact, bonding vs antibonding orbital of Valence Bond Theory starts with the rough approximation that , bonding orbitals bring electron between two nuclei more and antibonding less. You may also think that question- Why Li, Na, K, etc. cations are more stable than elements as the liberated electron has to overcome electrostatic attraction? The full-orbital stability is also far beyond the scope of coulumb's law
You are mistaken.When they are close,atoms and also molecules repel each other since the outermost electrons are negatively charged,and the closer the atoms or particles are,the greater the repulsion is.All this can be found in textbooks with abundant details.
To understand why atoms can join into molecules despite general repulsion between the outermost electrons in atoms, you need to study covalent bounding. Read chemistry reference works. All of this is clearly explained in these reference works.
The fact is that the electron trajectory is "smeared" over the space around the nucleus. On the example of the Hydrogen molecule: The force of attraction of each proton to the nearest part of the alien electron cloud at a short distance is balanced by the forces of repulsion from the second proton.