Is there a specific term for words like ふわふわ, ぺらぺら, and 人々?
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畳語. Though I dunno if you’d use that term in usual day-to-day conversation.
The first two are also オノマトペ 
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Onomatopoeias are sound words right? So are all onomatopoeias in Japanese 畳語?
Nah, there are plenty that are just a non-repeating sound like ほっと or じー or はくしょん.
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BTW, there are whole books of them. Found this is a book store in Osaka, and there’s more than one such book.
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For onomatopoeia, there’s also this site (here’s ぐちゃぐちゃ for example), which is one of my favorite sources to mine for flash cards because it has an image for each of the onomatopoeia pages along with definitions and example sentences in Japanese with English translation.
I own a huge onomatopoeia dictionary called 擬音語・擬態語4500 日本語オノマトペ辞典, which I reference surprisingly often! The dictionaries I have installed on Yomichan don’t really do a great job with onomatopoeia, so I struggled a lot with them before I started looking up their definitions in Japanese.
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Wow, 4500! 
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