After this card leaves the battlefield, is the effect still in place? Does the effect still put an extra +1/+1 counter on a creature if it's the chosen creature type?
Permanents only have their effects while on the battlefield, unless the ability in question specifically says otherwise.
That being said, the counters, once placed, are independent of the Mimic itself; if Metallic Mimic dies, any counters you've already gotten stay. You just won't get any more.
After this card leaves the battlefield, is the effect still in place? Does the effect still put an extra +1/+1 counter on a creature if it's the chosen creature type?
That being said, the counters, once placed, are independent of the Mimic itself; if Metallic Mimic dies, any counters you've already gotten stay. You just won't get any more.