Using xiànzài and zhèngzài in a single sentence
"现在", "正在", "在" all have the meaning of "now", but have slightly differences. "现在" is more like "nowadays", "正在" and "在" are equivalent to me, they are all like "-ing" in English. "现在我正在学汉语" sounds like "Nowadays I'm learning Chinese".  "我正在学汉语" means "I'm learning Chinese". "现在我学汉语" is weird, it's like "Nowadays I learn Chinese".  And you are right, as a Chinese, "正在" and "在" are equal to me if you want to use them to express "-ing".