I'm thinking of doing an extremely long (and therefore slow speedrun). How would you go about doing that? Do you just need to constantly keep recording segments and uploading it? Most sites have a limit on what they save and if streaming, there's a good chance stream would end sometime in those 41 days. I have the means of making a game run and whatnot during that time, but how should I document/record it?

I'm assuming this category doesn't already exist, or you'd be asking the runners/moderators of that game what's expected.

So if you're going to be the first doing this particular run, you could check out other super long runs and ask those runners for a guideline, such as Baten Kaitos 100% and the other runs listed in this thread.

I'm not sure I get exactly what you're asking. If you mean the recording may get interrupted by disconnections, I advise you to get a capture card. If you mean you'd get very tired, well, you probably could take a few minutes of a break during the run if you really need it. Unless you stop the timer, I think mods won't have any problem with that.