A bunch of quests state "if the heroes win then the next quest is......" and same if the overlord wins. Can the winner still choose a rumor quest instead? Probably but has that been addressed?

The rumors are entirely separate from the campaign quest tree. That is, they do not affect what the "next quest" is. I see it as no different than "after completing 3 act 1 quests, players proceed to the interlude," since that means, "3 quests and maybe some rumors, proceed to another rumor or the interlude."

All Rumor/Advanced quests that are in play can be selected instead of selecting the quest for the campaign. Remember that those quests do not count as completing quest for the campaign, they are all essentially "bonus levels".

I know they don't count.

I know they don't count.