Others have already gone but feel like going.
1. No there are other ways, though darkcorp probably still represents the latest take on that whole line of thought. darkcorp is one of the methods that works by replacing every IOS with a customised version (colloquially known as cIOS in the homebrew scene).
IOS for those playing along at home is the sort of low level operating system/firmware underpinning the wii. As games struggled to be updated on the Wii (there are very few examples of anything software based here, and that all for Nintendo in house stuff as far as I am aware) then rather than trying to keep all old games working with new IOS versions (basically impossible as all manner of new hardware and possibilities that were unknown at the time of launch could happen) Nintendo instead opted to make new versions and games could pick the one they wanted to use.
If every IOS is custom then the disc channel in its naive load the relevant IOS would in turn load a customised version. Or as mentioned you could hack the disc channel by various means to load everything to a specific IOS (I think homebrew types just about managed to get everything running on one, but most would bump it to three to handle the different hardware options some games saw for maximum compatibility as it were).
To finish out things then mIOS is the gamecube backwards compatibility layer. There are custom versions of that, though there are also other ways to run gamecube games.
2. There are revisions of the wii you can use a hidden 3x read mode (compared to stock/mod chip 6x, though optimisation helped) to use with burned discs sans modchip. Later revisions dropped it though. Also 3x,6x... USB and/or SD which is available to all but those with those stupid family wii and wii mini models (give or take some not inconsiderable hardware hacks) is faster by a considerable amount so people generally suggest that as an exclusive means.
3. Neogamma is its own program and as far as I am aware has no recourse to alter the disc channel.
4. No, it should run fine with the solitary modded IOS/CIOS. No need to mod all of them.
5. Same as it ever was really. As above it is a fairly massive change compared to the more surgical approach of the typical install with greater scope for screw ups. Use a proper installer and the main concern (other than certain homebrew not working properly) would be the increased time taken to mod increasing the chance of a power cut happening at a critical point, though if your wii supports boot2 bootmii or you have similar restorative options from some other means then eh.
In a blow to my credibility I don't know what happened to some of the BCA stuff that various Nintendo first party games used as much of it became obsolete around this point (was dangerously close already) and I observed more from a distance after this.
6. There have been various forks, attempts to update, attempts to replicate (many IOS installers can be made to replace all IOS with custom versions of whatever base the like, which would include functionally replicating darkcorp, cioscorp and other things in this vein but also with more modern cIOS takes, and there have been some that are still ongoing to this day squashing little bugs and annoyances mostly). 1.1 I believe is the last generally "official" one, various people suggesting some forks, no forks as far as I am aware* are as good as one of the better homebrew installs that do the functionally thing if you are insisting on this path.
*the ?corp approach died off in the mainsteam wii hacking scenes very early on but there might still be some dark corner of an unknown forum somewhere where it was considered unfairly put out to pasture.
Re: apps that rely on stock IOS/hackmii installer. To the best of my knowledge all the trouble apps here are obsolete really save for the hackmii installer that is artificially restricted to needing stock, though it was done to save them headaches form weird and wonderful IOS combinations that people might cook up. As many people consider it an essential part of a homebrew machine then you get to debate the tradeoff of not having it, or having it to install and then replacing all your IOS with cIOS and calling the homebrew channel (which I think was mainly concerned about having a stock IOS30, though sadly a popular IOS to use) a wash.
Final note. If you will permit a proverbial take you by the shoulders and shake you .
I get the appeal of using the "official" disc channel, I get the appeal of neogamma (believe me I love boring and basic text lists to select from an go rather than the fancy animated covers, art and whatnot favoured by many in the wii scene if the other loaders are anything to go by). Let go of "comfortable" and embrace stuff that actually works™. This means look into what large SD card and large USB options can do for you, sadly nothing is quite as basic as neogamma in that but you can still largely effect a text list. Your 4 year old sibling and 104 year old grandpa can learn to navigate a loader (assuming you don't have forwarders and such installed to make it even easier) and you certainly can too.
At some point someone might come back, realise the Wii is basically dead (nobody is expecting updates at this point, and if somehow there is one to probably sort some silly privacy or payment laws that pop up for a technically active service. Compared to back when then updates were every few months which mean redoing hacks for all those which is tedious), the Wii U is dead (it also benefited from custom IOS, see vWii, so that can trouble some aspects here), homebrew has reached a settled/stable point for the most part and thus construct some kind of best of all worlds with fully custom cIOS, easy wiiware/vc, suitably modified versions of installers/homebrew channel that don't care (assuming it is not a whole new menu setup), recreate whatever installers various flavours of ROM hack wanted to use over patch the disc/iso/files within approach, modded disc support where relevant, hopefully modded menu to allow no need of a wiimote/sensor bar to select for gamecube controlled stuff... Pending that glorious day (by the way offer of beta tester for one going for that) then just go with handful of cios, bootmii boot2 if you can, USB/SD loaders and such that is the mainstream way.
https://wii.guide/ https://sites.google.com/site/completesg/ https://gbatemp.net/threads/best-wa...i-for-windows-official-support-thread.207126/
All those should get it done fairly painlessly.