(Now that I've sort of figured out how to generalise Fajans' rules, I feel less frightened about writing the articles on the other main groups. Maybe I can, as I promised myself in 2011, get them all done before the decade is out!)

I sincerely apologise for neglecting carbon here. My excuse for doing so is that the chemistry of carbon is pretty sui generis. There is no other element that is anywhere near as versatile. I'm rather with Carl Sagan when he said that he was a carbon chauvinist despite not being much of a water chauvinist. If I consider all the things I said about boron, none of them are true for carbon, because carbon has as many valence electrons as valence orbitals and is quite happy. Sure, carbocations form, but mostly as reactive intermediates (and given the existence of NH₄⁺, H₃O⁺, and H₂F⁺, is that really much of a disqualifier?); C(OH)₄ (orthocarbonic acid) and its salts are all unstable and have never actually been experimentally detected; and we know very well what carbon bonding and carbon hydrides – never mind that H and C have similar electronegativity anyway so that the C–H bonds are not polar – are like from high school. This is doubtless because already the +3 charge is too high to be ionic for boron; what hope can we have for carbon as a supposed tetrapositive cation, then?

This being said, I do have something to say about Si, Ge, Sn, and Pb. If I may be pardoned some generalisations:

1. The chemistry of group 14 may readily be rationalised if you assume that electronegativity decreases down the group as Si, Ge, Sn, Pb. This is naturally a bald-faced lie, and I am simply making it more convincing by refraining from linking to electronegativity to show how wrong this is (oops). But this is partially because electronegativities are most usefully compared when the oxidation state remains the same, and the problem is...
2. ...that the oxidation state does not stay constant down the group. Si^IV of course dominates, but already Ge^II is gaining some ground; by Sn^II we have the lower oxidation state stable in aqueous solution, and Pb^II is the most stable state. This is important because metallic character not only increases with size, but also with lowering the oxidation state, and this gives these elements a double dose of increased metallic character thanks to relativity (which of course giveth and taketh away thanks to the lanthanide contraction).
3. To some extent, hypoelectronicity is "revived" here because of the possibility of expanding the octet. If we use the old d-orbital explanation, we even have real hypoelectronicity.

something about P, As, Sb, Bi

King order:

1. H
2. C
3. Si, Ge, Sn, Pb
4. N
5. P, As, Sb, Bi
6. O, S, Se, Te, Po
7. F, Cl, Br, I, At; He, Ne, Ar, Kr, Xe, Rn
8. B
9. Al, Ga, In, Tl
10. Be, Mg, Ca, Sr, Ba, Ra; Li, Na, K, Rb, Cs, Fr
11. Zn, Cd, Hg
12. Sc; Y; La, Ce, Pr, Nd, Pm, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu; Ac, Th, Pa, U, Np, Pu, Am, Cm, Bk, Cf, Es, Fm, Md, No, Lr