For the forum home page view, that's controlled by the forum software. A forum can't exist in two places at once, so one of the places the forum acts as an actual forum showing the info, and in the other place it acts as a forum "link", and the link doesn't have all the recent info like last post and all that. Moving the sponsor forums to off topic was to increase their visibility. I'm not positive what would happen if I moved the sponsor forums back to the main page and made the off topic table forum links (meaning I'm not sure if they'd even show up with the modifications I made to have them displayed), but if they did they would show the info the same way it's display currently on the main page.
As far as I can tell it's a one or the other situation, but I'll take another look to see if there's a different way to have a link to a subforum that acts more like the actual subforum.
I'm pretty sure the red buttons work, at least I seem to recall seeing them as full red in the past when there's new posts. I'll do a bit of testing, I don't think there's a reason they shouldn't work but it could be my modifications are incorrect.
Uncertainty is an uncomfortable position.
But certainty is an absurd one.