I can't answer all your questions, but I'll do the best I can:
For many years, the Homebrew Channel (HBC) has been the de facto standard for launching homebrew. The only thing that has really changed is how the channel is installed. At the current point in time, there are a reasonable number of exploits available for use with everything up to the latest version of the system software. The compatibility table here shows all the current (and indeed, past) exploits: [
wiibrew.org]
Team Twiizers (TT) have just launched in the last few days an updated version of HBC actually (the update was to add support for the Wii mode of the WiiU, but it also works on the Wii). TT aren't working as much on the Wii as they were at one point, but that's largely because they don't need to; HBC in it's current state works very well, and Nintendo haven't launched any update for the Wii to block current homebrew efforts in quite a long time. It looks unlikely there will be another Wii update.
TT aren't (solely) responsible for devkitPro though; many, many people, including TT members, have contributed to devkitPro over the years. An individual called WinterMute takes on the task of maintaining devkitPro. As for whether it bears similarities to the official SDK; sadly, yes. There are parts of it ripped right out of the official SDK (my understanding is that no one ever bothered to properly reverse engineer certain things, so WinterMute just ripped the relevant sections from the official SDK). Unfortunately, this means the legal status of anything built with devkitPro is questionable, but that is generally ignored by the homebrew community. Most people aren't even aware of this I don't think. It's still better than other scene's where there is no homebrew SDK and leaked official SDKs are the only choice (e.g. xbox).
As for how it came to be: Most of it was reverse engineering of existing code. Figuring out how things work, then writing code to do those things. As I said, some portions were ripped from the official SDK.
Hardware is all controlled by "IOS". To understand this, you need to know that there are two processors in the Wii: A PowerPC and an ARM. The PowerPC is what runs the code you see, e.g. System Menu, games, homebrew. The ARM runs code called IOS. Basically what IOS does is give the code running on PPC access to the hardware, and also implements the security system. So for PPC code (e.g. homebrew) to access the various hardware, it basically has to "ask IOS". These IOS requests are wrapped up nicely in the functions of libogc (the Wii part of devkitPro), so programmers don't really need to worry about this. But essentially IOS contain the hardware drivers, and we can use those drivers from PPC code to do whatever needs done.
Stuff about game engines and libraries etc., I don't really know, as I'm not a developer. Hopefully someone else can pop in to answer that.
As for contributing to devkitPro, you can submit patches I believe, but it is an SVN on sourceforge, and I don't think that's going to change anytime to soon.