I've griped more than once about the
Iroquois in the past, and I still stand by my ill feelings on the civ's design. To start, the Iroquois' kit is hard focused on Forests/Jungles- the UA treats Forests and Jungles as Roads/Railroads (complete with

City Connections) and grants all Military Units with the Woodsman promotion, the UU gets 20% CS in Forest/Jungle, and the UB adds additional yields to Forests/Jungles as well as Camps and Plantations (most of which would be in Forests and Jungles). While this certainly makes them very powerful with a Forest/Jungle heavy start, and regions with large swaths of Forest/Jungle, the thing is how
often do you actually start with substantial Forests/Jungles? Let alone spawn in a big enough region covered with the terrain to truly make a Wide empire, be it through settling or conquest. In all my best games with the Iroquois, I only had enough Forest and Jungle to settle five or six cities before having to resort to locations lacking Forests/Jungles, and none of my enemies had enough Forests and Jungles to capture with the Mohawk Warriors. VP certainly improved the Iroquois from how they were in Vanilla Civ 5, but I still feel like you'd have to play in Aborea or YNAEMP TSL to have a chance at winning as the civ since only in those maps do you have forests aplenty. And the increased CS near Natural Wonders is just baffling to me: not only is it even more terrain dependency to the Iroquois that often doesn't work out but it's not even thematic with their history. The
closest Natural Wonder to the real-life Iroquois is Niagara Falls, but from what I can glean that location was never really significant to the people. Such a component would make perfect sense with, say, an Aboriginal Australian civ due to Uluru, but not so much the Iroquois.
And on the note about thematics, the positives of the Iroquois' components mainly gear them for Domination (having huge production and high CS Units, but not much science, culture, etc). Which yes, does fit with the Iroquois Mourning Wars and immense brutality to neighboring tribes and white settlers. But the leader of the Iroquois in this game is
Hiawatha, a man who famously
hated war, vocally advocated for
peace, and even became a disciple/representative of the Great
Peacemaker, with whom Hiawatha would make the "Great Law of
Peace" that founded the Iroquois Confederacy... Like, I know a Civ needn't reflect a leader's agenda, but the leader is still a big influence; is France's conquest-focused UA not because of Napoleon Bonaparte being the civ's leader in this game? But even then, the "Great Law of Peace" in itself is a more unique aspect of the Iroquois than benefitting from the woods, is it not?
The Great Warpath was used by many Eastern Woodland natives, not just the Iroquois, and many civilizations around the world made use of forests (be they temperate or rain) to defeat their foes, such as Vietnam. But only the Iroquois have something like the "Great Law of Peace", turning the five warring tribes into a close-knit and dedicated confederacy that lives on to this day. ...So yeah, Iroquois are too RNG dependent to be fun and their kit isn't really accurate to the real-life civilization, or at least the leader represented in-game.
For the second, I'm gonna have to chime in with pineappledan in finding the
Ottomans poorly designed due to their UA being at odds with their UU and UB. You gotta complete trade routes for big yields, but you wanna go to war to take advantage of the UU and UB bonuses, and being at war tends to result in very dead trade units or at least having much less targets to trade with. Not sure what could be done with the Ottomans UA to make it better, as I'm unfamiliar with Ottoman history other than "they were
very good at conquering stuff" and don't know what dedicated warmongers need aside from "better military units", but pineappledan's suggestion looks very good.
For number three... Well, I wouldn't call them poorly designed, but I admit to having great difficulty understanding how to play
China. They benefit from settling/conquering cities and making Great Works, that much is obvious, and they essentially have a better WLTKD. But they lose half of the yields they get from their UA on advancing eras, so I guess I'm supposed to delay advancing eras as much as possible? And the UA seems to gear them towards Wide-play (via Progress or Authority), yet the use of Great Works and abundance of food/growth is for Tall-play. And indeed, a guide I read recommended going Tradition as China, yet suggests settling cities like crazy...? And that's nevermind what policies and such you take with China after the Ancient Era ones, which just stumps me. I tried to play that Civ many times and it never works out. ^_^;
And for a quick tangent, I'm kind of surprised that the Shoshone are being deemed bad recently. I can agree to not liking their dependency on ruins, but the landgrabbing is honestly one of the more powerful parts of their kit: you can snag resources and lucrative features, such as Atolls and Oases, just from settling (whereas I often have to purchase such tiles because the "culture acquisition" keeps going for bare Grasslands or Plains tiles), which is especially good if a neighbor was blatantly aiming for those. And the increased CS in owned territory makes you the ultimate turtle. But then, I do suppose that the Shoshone lack any real path to a victory condition, having no bonuses to Science, Culture, or Diplomacy that the defensive boost would really help with. So I guess either the Shoshone UI could have its Culture yield increased to give them an edge in CV, or replace the Ruins bonus with anything else to give the civ an edge in SV, CV, or even DipV.