Do only outer electron shells take part in forming chemical bonds?
Great Question. 
From this article, it seems that extreme conditions of pressure can lead to new type of molecules,bondings and how the electrons participate in the bonding.


  Under very high pressures, it appears, electrons in the atom's inner shells can also take part in chemical bonds.
  
  “It breaks our doctrine that the inner-shell electrons never react, never enter the chemistry domain,” says Mao-sheng Miao, a chemist at the University of California, Santa Barbara, and the Beijing Computational Science Research Center in China. Miao's calculations show that under extreme pressures cesium and fluorine atoms can form exotic molecules with inner-shell bonds. 
  
  Miao identified two molecules that, at high pressure, would involve cesium's inner electrons as well. To form cesium trifluoride ($\ce{CsF3}$), a cesium atom would share its single valence electron and two inner-shell electrons with three fluorine atoms. Four inner electrons would go into making cesium pentafluoride ($\ce{CsF5}$). 
  
  “That forms a very beautiful molecule, like a starfish,” Miao says. He reported his findings in Nature Chemistry. Both the shape of the resulting molecules and the possibility of their formation are “very surprising,” says Nobel Prize–winning chemist Ronald Hoffmann, a professor emeritus at Cornell University.


Found this in the comments about the stability of the exotic molecules at normal pressures


  "Since the compound is thermodynamically unstable it would decompose to the more stable form at lower pressures. Since this means that they are going to higher states of enthalpy I would expect that this decomposition would be a endothermic reaction which means that they would get cold during the process."