Wow, there is a lot here. I applaud you for the efforts to improve what is already a great game and community. I'm sure you will get a lot of great ideas from the smart/hard working people on this forum.
Website
Nobody views the site. Or if they do, they don't read it. Or if they do read it, they don't understand it. Etc.
For example, new people keep missing that we have a FAQ, or a wiki, or a bug tracker, etc. I don't really know how to fix this without changing the theme or cluttering up the menu. Or maybe it's hopeless.
I'd like to give your whole post some more thought and provide some more worthy feedback, but off the top of my head, the
https://openxcom.org/ website seems like a good place to start.
First, combating the issues you mention certainly isn't hopeless. If you want more people to explore the website and read what is there, it would need to be organized a little different and possibly even get a facelift. The most important information for a new user is in the "About" section, but that's one menu item out of many and the FAQ section is buried a few scrolls deep within that section. You start in the "News" section and none of that info means anything to a first time visitor.
Also, like half the links in the sidebar menu take you to other websites which have a whole bunch more info and links and it's just total information overload and a new visitor could be easily overwhelmed. Some people who aren't totally motivated (or lazy) may just leave rather than read and click around to find the important info. If you click "Mods" for example, you go to a website that has absolutely no explanation or description where not even everything works (as you describe, you're sending people to a "dumpster fire".)
So I think the main OXC website could be completely redesigned/organized. This would be work, but I'm sure people here (myself included) would be willing to help.
However, if you're hesitant on doing too much with the main OXC site,
the biggest thing I think you can do is steer people to the Nightlies instead of 1.0. Really, there is no reason anybody should be playing 1.0 at this point. The Nightlies fixes so many issues from that version and has so many more features. Plus, the majority of mods (certainly no actively updated mods) even work with 1.0. But currently, if you're a first time visitor, based on the descriptions on the main page, you would think that 1.0 is the best place to start and the Nightlies looks a little uncertain. I mean, even the term "Nightlies" isn't 100% clear to those not familiar with open source projects.
My thought would be to either:
1) Take the most recent 100% stable version of the Nightlies and call it 2.0 and just replace 1.0 all-together.
2) Change the setup/language to strongly encourage new users to use the Nightlies and discourage 1.0.
I think that's a good starting point which is an easy change. Then redesigning the site could be a longer term project.