Egg #3: You can use any pokemon, however, for four of them you cannot use any set listed on the pokemon's Smogon analysis. For a set to be considered legal it must use two or more different moves and a different item than that in a specific set.
Example:
Set Specified:
Rotom-W @ Leftovers
Ability: Levitate
232 HP / 56 SpA / 220 Spe
Modest Nature
~ Volt Switch
~ Hydro Pump
~ Will-O-Wisp
~ Pain Split / Hidden Power Ice
Changed:
Rotom-W @ Life Orb
Ability: Levitate
252 HP / 4 SpAtk / 252 Spe
Timid Nature
~ Substitute
~ Pain Split
~ Hydro Pump
~ Thunder Wave