You can double activate the ability the way you described, but you won’t be satisfied with the result. We have a new rule that says if an ability wants to transform a double-faced card, but that permanent has transformed since that ability was put onto the stack, the instruction to transform the double-faced card is ignored [CR 701.25f].

No. The converted mana cost of a double-faced permanent’s back face is now calculated as though it had the mana cost of its front face [CR 202.3b]. Even though you can’t see it without turning the card over, Perfected Form’s converted mana cost is 4.

Yes. Clone isn’t a double-faced card, so its converted mana cost is converted the old-fashioned way: by looking at its mana cost [CR 202.3a]. Except that Perfected Form doesn’t have one. The converted mana cost of this Clone is therefore zero.

Unfortunately, you can’t keep it around. This is where the rules for this get kind of weird. Perfected Form’s converted mana cost is 4 because there’s a rule that says when you’re determining the converted mana cost of the back face of a double-faced permanent, you calculate it using the front face’s mana cost. There’s no similar provision for determining the mana cost of a double-faced permanent, so Perfected Form just doesn’t have one. Because it doesn’t have a mana cost, paying that cost is an impossible action, and you’re forced to sacrifice it [CR 117.6].

As Altered Ego resolves, the game checks to see if there are any replacement effects that need to occur. Altered Ego’s effect applies here and makes it a copy of Apocalypse Hydra and puts 5 counters on it. Then, the game checks for replacement effects again [CR 616.1e]. Altered Ego/Apocalypse Hydra’s new ability now wants to put X counters on it. The value of X is usually the same throughout a card, but in this case, because Altered Ego gained this ability, the value of X is 0 [CR 107.3h]. Altered Ego enters with only 5 counters.