What trends exist in the Periodic Table?
You are correct on atomic size being due to number of electrons
and their shells and the reason why atomic size decreases from
left to right is due to the number of the protons being greater
on the right than on the left of the periodic table with same number of shells due to shell theory. (Reference).
The concept you are forgetting is
Valence Electrons.
Atoms are stabilized most often when there outer most shell is
filled with 8 valence electrons (except for hydrogen and helium with
0 or 2). The elements on the left side of the periodic table lose
electrons easily since they have a very large atomic radius allowing
for lower ionization energy. on the right side of the periodic
table(nitrogen, oxygen , and halogens) have a smaller atomic radius
creating a stronger pull making it harder to lose an electron thus
they will steal an electron to become stable. 
The best way to summarize this is to quote Chemistry.about.com 


  "There are trends in
  metallic character as you move across and down the periodic table.
  Metallic character decreases as you move across a period in the
  periodic table from left to right. This occurs as atoms more readily
  accept electrons to fill a valence shell than lose them to remove
  the unfilled shell. Metallic character increases as you move down an
  element group in the periodic table. This is because electrons
  become easier to lose as the atomic radius increases, where there is
  less attraction between the nucleus and the valence electrons
  because of the increased distance between them."
  (Reference)
  Positive ion size decreases due to the lack of electrons which allows for the protons to pull stronger on fewer electrons.
  The inverse applies for negative ion size. Due to the fact that there are more electrons, the size will increase since they will occupy more space.
  Electronegativity is the pull a elements has on electrons. This determines how it bonds with other elements i.e.(whether it shares or looses electrons). If a element has over a 1.7 Electronegativity difference then these the element with the smaller electronegativity will give away several electrons 1-4. Elements on the left side of the periodic table have the smallest Electronegativity due to their atomic size and inability to gain enough electrons to be stable ions. Elements from left to right in a period show increasing elctronegativity, and electrons form up to down in a group will have a lower electronegativity. Also fluorine has a 3.98 elctronegativity. (Reference).