The "morph" in "xenomorph" as a purely Greek scientific jargon construction mostly just means "shape". It is interesting in English "morph" as a verb has come to mean "change shape", and it is possible the users of the term in the franchise do intend that. But technically if that were the intended meaning it would be something closer to "xenotransmorph".

The use of the term "xenomorph" in the film predates the development of the morphing technology, seen early on in Willow, The Abyss, and it largely entered popular perception after T2 in the early 90s. So: no.

Same morph as in polymorphism.