Yes and yes.
And when it re-enters it can copy a new creature. (in case you already killed the previous one)
In fact, if you don't copy something, it'll just be a 0/0 with a +1/+1 counter on it named Evil Twin without any useful abilities. (It will have its entire copy ability, but it won't do anything and you cannot destroy other Evil Twins with it, because thats part of the copying effect, which you didn't use in this case.)