Is the subject always in the first part of the sentence?
In English, the most common pattern today is certainly with the
subject in the beginning of the sentence; and it is certainly true
for simple sentences: "Edmund Hillary climbed Mount Everest" --
where Edmund Hillary is the subject. One can interchange subject
and object by using passive voice: "Mount Everest was climbed by
Edmund Hillary". But in that case the subject becomes Mount
Everest, and it still comes first. The most likely constructions
with the subject at the end are going to be archaic or poetic,
"Into battle rode the five thousand."
It is true that it is the most common pattern, but a good writer
varies their sentence beginnings.
Original Sentence: I feel peace and calm when I look at the
water and hear the waves. Looking over the water and hearing the
waves, I feel such a peace. When I look at the wate and hear the
waves, I feel peaceful. Relaxed and calm, I look at the water and
feel at peace. In short, NO the subject is not always in the first
part of the sentence.