Zapdos is an electric flying Pokémon. The abilities that it learns are pressure and lighting rod. The lightening rod is actually a hidden talent.
Zapdos doesn't learn it by leveling up. You buy or find TM24(Thunderbolt) and then teach it to Zapdos.
Look here: http://bulbapedia.bulbagarden.net/wiki/Zapdos(Pokémon)#Learnset
Zapdos does not learn a 1-hit K.O. move leveling up in any Pokemon game.
level 85
The same reason a Bulbasaur can't learn Flame Thrower. Type incompatibility. Zapdos is a electric/flying Pokemon and Solar Beam is a grass-type move.
Zapdos will not learn many moves, but here are a few moves such as: Charge on level 61 Light Screen on level 73 Thunder at level 85 Hyper Beam by TM15 Shock Wave by TM34 Hope this helped you and your Zapdos!
Zapdos will learn Thunder on it's on sometime around level 60.
I think you have to use a TM on him.
Zapdos never does learn Sky Attack. The best ways to get it to learn it, is to trade it over to either Pokemon XD or Leaf Green or Fire Red. You can also just use GameShark, I am actually looking for an easier way myself.
zapdos can learn peck, Thundershock ,thunder wave,detect, pluck, Ancientpower, charge ,agility ,drill peck ,thunder, discharge, roost, ligth screen, and rain dance
you can only get zapdos in fire red and leaf green but in there he is lvl 40 i think
Zapdos does not learn zap cannon via level up or through any other means in Generation IV. It used to be able to learn it via TM in Gen II, so I suppose you could trade one from there if possible