It's been some years since I downloaded "Stuffit", but I don't recall ever trying to (or needing to) open "Stuffit" itself. "Stuffit" is used to open (decompress) certain files that you would otherwise be unable to open, so the only time I use it is when I'm prompted to (automatically) when opening a .zip file or something like that. Maybe you know all this, but it sounded like you were trying to open "Stuffit" after you downloaded it, which didn't seem to make sense to me. So, if you downloaded "Stuffit" successfully, the next step (following Mr. Dye's advice) would be to try downloading Mozilla again, and choose Stuffit when you get to the step that calls for it. If there is indeed a version of Mozilla for 8.6, then there's got to be a way (I would think) for you to successfully download it.
Beyond this, the best advice I can give is... go to the nearest white courtesy phone and page Mr. Dye. Seriously, it might be helpful if you took detailed notes during your attempt to download Mozilla, and that way it might be easier to get help here from the guys who are computer savvy (not me).
Hope this helps.