So the Emperor is assassintaed, but what will become of the Empire?

Did he have children?
Who will take the throne?
Will the Empire decend into (more)chaos?

Most likely the highest elder of the Elder Council. I don't believe Mede II has an heir, at least one that we are aware of.

No named heir, even if there is an heir that heir will either die or become nothing more then a puppet for his Elder Council master, unless of course the heir arranged for the murder in the first place.

As for the other questions, I have no idea. You'd hope that people in the Elder Council have a plan at the ready, and that they have another Emperor standing ready to take over. If not a Civil war in Cyrodiil is pretty much inevitable. My hope is, that this a plan to unite Hammerfell and Skyrim back into the Empire and take the fight to the Thalmor. However it's just as, if not more, likely that this is just a way for some Elder Council members to take power and they might just ignore the entire state of the Empire for their own selfish gain.

It is generally accepted the Emperor dies even id the Dovahkiin decides to destroy the DB? (I know it's highly unlikely Bethesda would go with this as a canon situation unless they pull off some Dragon Break but still)

The Empire will die, regardless of who destroys the DB.

Remember if you destroy the DB not every member is there. The little vampire girl, I forget her name, Cicero and thus the Night mother are not there. The Emperor could still have been killed then.
If you do follow the entire quest line then the DB still gets nearly destroyed, and only two or three members remain (depending on what you did to Cicero).

Regardless of which the Emperor will end up dead, and the Night mother will survive.

I'm not sure that the Empire will die, but since the DB quest-line is very likely to be cannon we can assume the Emperor was killed. The Destroy the Dark Brotherhood is probably one quest that is just "thrown in" as an afterthought for those who complained about not being able to destroy the DB in Oblivion(though I am very glad they added it).

Sorry meant Emperor... The Emperor will die regardless of your choice. Bethesda always assumes all quests that are possible as canon, or finds a way to ignore conflicts between guilds (great houses in Morrowind, dragonbreak in Daggerfall). You can't really ignore something like the Emperor dying, so he's dead.

If the Dovahkiin is Tiber 2.0 as I believe he is, then it could be him.

How is Bethesda supposed to pull of a unknown character of unknown race six skill and age to suddenly become the emperor? The emperor generally speaking is a rather public figure, books will be written about him/her, people will talk to him/her, I just don't see this happening...

Not unless their is some kind of mantling involved. But even then, one of Talos his greatest achievements is leading and creating the Empire, it would be hard to mantle Talos without doing the same thing.

Well, one solution would simply be to avoid mentioning the guy in later games. We don't even know who Titus Mede II's father was, if he had children, if he had a wife, if he had siblings. While these are certainly people who would be recorded, (and whose absence would be noted) they go unmentioned.

Though I don't really see it as very likely. My guess is that we'll either get a reasonable exit for the dovahkiin in a expansion (i.e.the CoC) or his disappearance will be handwaved. (Nerevarine by rumor, Daggerfall agent by fan [censored])