Question on two Paragon skills.

Does "Find their weakness!" and "Go for the eyes!" work on wands and staves? Or only melee weapons? Are bows and spears considered melee?

Yes, those skills work on any weapon including wands and staves.

No, bows and spears are not "melee." They do physical damage which can be an important distinction, but they are not melee.

Also an important distinction is if a by default physical weapon is upgraded with an elemental mod (like a bow with fiery bowstring) it no longer does physical damage but elemental damage.

1. Spellcasting weapons: staff, wand.

2. Martial weapons:

2a. Melee (close-combat) weapons: sword, axe, hammer, scythe, dagger.

2b. Ranged-combat projectile weapons: bow, spear.

There is one touch-ranged spear attack described as a "melee" attack, but general melee attacks, such as Wild Blow, do not work with spears.