When you buy any GP5 as your starting item, it will immediately start generating gold, even when gold gain is disabled, it's not exactly a critical bug but i'm just pointing it out
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Mordekaiser's pet will aid in capturing altars, is this working as intended?

For your second question, I'm sure this is intended as Riot made it like that because they only made it with Morde's pet or Yorick's and not with pets like Mal'z voidling, so I guess that's right.

Yorick and Morde pets are considered champions for all intents and purposes.

Except capping in Dominion, of course.