For one of the example sentences given, 生徒毎に紙を渡した
Can we use 各 instead?
各生徒に紙を渡した
Does it change the nuance of the meaning?
I guess the change in nuance is かく is focusing on having handed one out to each student in particular, whereas ごとに is emphasizing the repeated nature of the handing out itself.
I don’t personally know if there is practical difference in meaning, but there is a subtle shade of nuance difference.