Once one of Marvin's abilities has been activated, it doesn't matter if the other creature you control with that ability leaves the battlefield; the ability still resolves.

If an activated ability of a creature you control that doesn't have the same name as Marvin references the card it's printed on by name, treat Marvin's version of that ability as though it referenced Marvin instead. For example, say you control Marvin as well as Floodpits Drowner (which has the ability ", : Shuffle Floodpits Drowner and target creature with a stun counter on it into their owners' libraries."). You would treat Marvin's version of the ability as though it said ", : Shuffle Marvin, Murderous Mimic and target creature with a stun counter on it into their owners' libraries."

Marvin gains only activated abilities. It doesn't gain triggered abilities or static abilities. Activated abilities contain a colon. They're generally written "[Cost]: [Effect]." Some keywords are activated abilities and may have colons in their reminder text.