Why are least electronegative elements usually in center of lewis structure
Why are least electronegative elements usually in center of lewis
  structure?


If there is a "central atom", then there are multiple (more than 1) bonds to the central atom.  If the central atom is relatively electropositive, then it will be better able to share its electrons and form bonds with other atoms, at least more so than an electronegative central atom would.  Also, electronegative atoms tend to carry multiple lone pairs of electrons.  If this electronegative atom and all of its lone pairs were at the center of the molecular structure, then we would have many more destabilizing (lone-pair - bonding pair) electron-electron repulsions, then if all of these lone pairs were on the periphery of the molecule.


  why are many molecules symmetric. Is there a reason why symmetry in
  nature and in chemistry is preferred over non-symmetry?


The symmetric arrangements (linear, tetrahedral, octahedral, etc.) minimize destabilizing bonding electron - bonding electron repulsions.  Remember methane is a perfect tetrahedron - that is the lowest energy arrangement because all of the bonding electrons are as far apart from one another as possible in this geometry.