Due to the close timing of Morrowind and Oblivion the protagonists may have ended up meeting with each other. Thoughts?

All the games up until Skyrim happen a short amount of time from one another. I don't see why not, if you want to have that take place in your headcanon.

Heck, through vampirism, maybe the hero of kvatch and dovahkin met

I believe it's stated somewhere in Oblivion that the Nerevarine left Morrowind for Akavir soon after the events of Morrowind. And was not heard from since then.

So it's unlikely.

Rumored. From people who barely know him in the first place. Its really just a handwave why the hero may not be there. Some people have legacy character which are the same person in each and every game.