For the max dmg of puppet's ulti, won't you need to count additional damage auras and spells to it? Like Revenant's Q, or Andromeda's damage aura, Wolf Commander's damage aura, Empath's As One, Ophelia's Nature's Wrath, or additional damage from items like Abyssal Skull? It's armor reduced by Sol's Bulwark, Shieldbreaker, Daemonic Breastplate and capping -armor with other ways (Pestilence ulti).

Additional questions: max damage of Mana Rift? Maximal amount of life gained on a single autoattack?