You can generally tell what group an element is in by their ionization energies.
For example (fake numbers to illustrate a point here
1st I.E. = 10kJ
2nd I.E. = 67kJ
3rd I.E. = 56KJ
The first electron came off relatively easy and then the energy required jumped up dramatically. You would conclude that this element is from group 1, since after its first I.E. it has formed its respective ion and a stable octet. Afterwards, since it is stable now the removal of subsequent electrons is much harder.
1st I.E. = 20kJ
2nd I.E. = 25kJ
3rd I.E. = 98kJ
4th I.E. = 110KJ
As for electron affinities you would use this for the elements which form anions. Example:
1st E.A. = 5000kJ
2nd E.A. = 2kJ
3rd E.A. = 1kJ
Once again, fake numbers but it illustrates the point. When the first electron was added a huge amount of energy was released. After that, it quickly died down. That means once the first electron was added, the element became its stable ion. So you may conclude that this was a halogen.
Electronegativities can predict whether two elements form covalent, polar covalent, or ionic bonds. Of course it is definately not a foolproof system as there are many compounds which do not comply to the numbers. Generally though you can determine the type of bond through the electronegative difference between two elements.
Difference of >1.7 = ionic
Difference between 0.5 - 1.7 = polar
Difference between >0 - 0.5 = low polar
Difference of 0 (diatomics) = covalent.
The only one for sure would be the diatomics which are truely covalent, the rest of the "covalents" are simply very low polar or polar. For example, sugar which does not conduct electricity in solution does not mean it is purely polar as it is not diatomic. It is low polar.