Turning a face-down creature with megamorph face up and putting a +1/+1 counter on it is a special action. It doesn't use the stack and can't be responded to.

If a face-down creature with megamorph is turned face up some other way (for example, if you manifest a card with megamorph and then pay its mana cost to turn it face up), you won't put a +1/+1 counter on it.

Deathmist Raptor's second ability triggers only if Deathmist Raptor is in the graveyard when a permanent you control is turned face up.

You choose whether Deathmist Raptor will enter the battlefield face up or face down as the ability resolves. You may also choose to leave it in the graveyard.

Megamorph is a variant of the morph ability. You can find more information on morph on cards with morph from the Khans of Tarkir set.