The "preview" for Halo Silentium basically proves that there are two Didacts. Didact (Ur), the one from H4 was the original but that leaves the other unaccounted for. Considering the preview coming from Silentium it appears there is also an unaccounted for evil coming our way which I believe will be something left (or possibly being) by the Precursors (possibly the flood, though I doubt it).
As far as Chiefs next AI companion. At the end of Halo Primordium the remnants of Guilty Spark is now looking for the Librarian whom he believes is very much alive. This will play a part in the game and I do believe Chakas will become the next AI of Chief. This will take a good amount of story to back it up as last time we saw Spark he was mad, killed Johnson, etc.
For those who have read the books (Forerunner saga), Halo 4 was outstanding in its delivery of facts we learned from the books and everything in between. I love(d) Halo 4 because of this (but again, I read the books which I recommend for those who have not as the game will make much more sense).
So we have some underlying questions coming.
1) The issue that will arise from two Didacts. One of which hates humans, and the other who cares for them.
2) Where is the Master Builder? He holds more authority than even the Didact and Librarian in Forerunner culture so he (Faber) will play a major role. Further, he is a major player in Mendicant Bias' orders and so on and he "supposedly" killed the original Didact which the preview of Silentium invalidates.
3) Guilty Spark (Chakas). What will his role be?
4) Elites vs Storm - My opinion is the Arbiter will come back but how? I feel their homeworld will come under attack by the Storm faction which will ultimately bring he and the MC back together in some form. Will the Shipmaster return too?
5) Librarian? She claims to be "all that is left" to the MC in H4 but Chakas/Spark seems to think she is very much alive.
6) Installation 3. Since we were introduced to it, will we be going there?
7) Geas. The Librarian insinuates that the MC is a culmination of years of geas planning. Considering that and the H4 terminals, AND the books what will we learn about MC. Is he a direct geas line of the Lord of Admirals, etc? My opinion is that he is. I say this because the Librarian claims the greatest enemy ever to face the Forerunners is "you". Now it can be inferred she means humans (which would be incorrect as the Flood would ultimately be the greatest enemy to the Forerunners) but Didact also states (book and terminal) that the Lord of Admirals is his "greatest enemy". We know that Chakas had the geas of the Lord of Admirals but we will see how this plays out.
Precursors. Silentium makes claim that there is a far greater threat awaiting out there than even the Didact. One can assume the only remaining possibilities are either the Precursors of the Flood.
I recommend people reading the books if they have not. They are really good (and I am not much of a reader, they just are outstanding).