I am wondering, according to our current understanding, whether life is completely deterministic. To begin with, consider a single-celled organism, do we have any evidence of any single celled organism deviate from the law of cause and effect ? This, same idea applied to us raises the question, whether we have free will.
If I understand your questions correctly, I would reframe it as whether life follows the laws of physics, in which case the answer is yes. Indeed, just how one defines life as opposed to other natural processes is still debated, see for example Erwin Schrödinger's "What is life?"
As to whether physics is deterministic, that depends on what you mean. Classical physics is precisely predictable if you have sufficient information, however, quantum physics has an intrinsic random component, and so could be said to be non-deterministic, although still following defined laws. As to questions about the nature of free will, I think that is better suited to a philosophy context.