Is CH2 an alkyl group?
It's generally called a carbene, which is very reactive with alkenes, forming cyclopropane.
In a molecule? I would call it a (1) methylene.
Simply put: no, it isn't.
An alkyl group is generally understood to be a stable substituent functional group, in other words, something that is attached to the carbon backbone of an organic species.
So in neither case would the term "alkyl group" apply.