Now, I'm new at this, so there's a chance I'm missing something, but I just can't wrap my head around this. On several occasions, I've seen people say that you can't build boats unless you're a Westernized country (or you just cheat like I did). Flat what. I feel like they're forgetting something important here. Plus, there's the issue I encountered while trying to play the Incan Empire, in which I would set a tech slider as far as it would go, only to be told that I wouldn't reach level 1 until around the year 5,000 (thank you, invest command, buggy though you are). Unless there's something wrong with my game, or this is addressed in an expansion I don't have, I don't see the point in even letting you play these countries if its not going to let you do anything but be conquered. I don't think this can be explained away as being "historically realistic", either— especially in a game so clearly designed to let you rape history.
More specifically, the native American countries get hit very badly by the "isolation" penalty. Basically, in addition to your techgroup (which already means you're paying roughly twice the base cost for tech compared to european countries, and remember that this is just going to increase the penalties for having the wrong sliders) you also get hit with a penalty for not having enough other known countries. Once the Europeans show up, the isolation penalty will go away.
Dunno what version you're playing, but you totally can build ships as any non-western culture, although your lower tech rates means the Latin cultures will outgun you badly after a few centuries (Polynesia never six-deckers, after all). It's also totally possible to play the native Americans, although extremely difficult. There are plenty of player accounts of doing so.
In the latest version of the game, countries under steppe horde government will be unable to build ships. As said, the low tech-rates of non-Latin countries are intended. You can undo this penalty during the course of the game by westernizing, though you may have to go through the process several times.
This has actually been changed in EUIV. It's possible as a New World nation to build ships, although the technology cost still hurts quite a bit. It's also possible, in theory, to invade Europe as the New World nations if you're ahead far enough - you just need to make sure you're ready for it.
IV: How come Corruption reduces Unrest, anyway? It doesn't exactly make sense from a game balance standpoint (especially since one of the major sources of Corruption is Overextension, which primarily serves the purpose of increasing unrest, so it feels like it's undercutting itself), so is it meant to be a Watsonian thing where it's like "those people don't officially have autonomy, but the administration is incompetent enough/open enough to bribes that they can basically do whatever they want, so they don't care?" Because that... also seems like a vast oversimplification of how "corruption" would affect a nation-state.
One of Corruption's modifiers is to increase the minimum autonomy in every province, which is rather bad.