I would also assert that any knowledge as it concerns nature would be vital to understanding your original statements.
To clarify. I put stress on excluding these far reaching phenomena because studying them will not alter anything we can observe on earth. Not to mean they are not part of it. It, nature, as you rightly stated, encompasses EVERYTHING in this universe. Both, to the physical eye, visible and invisible happenings.
One more thing I want to piece out further. The first disagreement you pointed out: I disagree that we are not part of nature.
I will try to state this as clearly as possible so there is no confusion as to what i mean. Earlier I stated that man is not a part of nature. But now I want to add that we are also part of everything that exists in this universe, which makes us a product of this 'nature' so to speak.
This may seem contradictory but bear with me. One very short answer is to point out that the human being you observe today is not in its original form. The human being as we know him today has already, for thousands of years, been subjected to direct influence of 'the human being'. Does this make sense?
We have already altered ourselves and our nature. Now, if these changes had been in tune with what was furthering, that is nature, then the human being you have today would be very different. So we could then draw inferences that oh, the human being is observed to do xyz, therefore xyz can be deemed natural. This last point was the very reason I wanted to make a clean cut separating human beings from the very beginning. I also alluded to things affected by man for the same reasons. Because it is common today, to infer that certain observations in nature are 'natural' when in fact they have already been affected by man.
To sum up:
we are a part of this universe and a product of nature (of God). But there is still a distinction between the human being and nature. Nature automatically follows a very definite course when left undisturbed. Man however, has the inherent ability to follow whichever course he decides upon (and he makes very many decisions in this regard). What is best for him will result from him adapting himself to nature. This will give him what he seeks which is bliss and happiness. Deviating from this, which he often does, will result in disturbances based on reciprocal action. Instead of learning from the results and making the right adjustments, well, you can judge for yourself...
Nature encompasses everything, including physically visible and invisible phenomena. I emphasized looking at what is right in front of us because we can learn the same thing from them. We didn't have access to them for tens of thousands of years, so it only make sense that what we must learn, we CAN learn from what has always been accessible. Not to say they are not a part of the whole..