1. There is a duplicate of 343 guilty spark that took control of an ONI ship and put the crew in cyrosleep (forgive me if that isn't what it is called). From what I understand, the clone is looking for the Librarian. I played spartan ops, but is she dead, or does Jul M'Dama have her?
Unknown. There is a possibility that she escaped Requiem in the conflict or had a slipspace 'bubble' similar to Onyx. OR ONIRF Trevlyan. 2. Will Jul M'Dama even have a role in the next campaign? If so, what? Obviously he has Halsey and all, but what will he do?
He most likely will, the Covenant will almost certainly make another appearance in H5, and Halsey being AGAINST the UNSC will be a factor. 3. What will Halsey's role be in the campaign if she has one which I think she will?
Most likely some kind of antagonist. She has half of the Janus key, so I can see a UNSC mission into getting that. However, Chief may also have 'Personal' Reasons to see her.
4. What will happen since Requiem is gone? Are the prometheans gone too, or are there other shield worlds where they are?
I doubt we have seen the last of the Prometheans. They may have been indoctrinated into the Storm, or be at other Forerunner installations.
5. What happened to the Didact? I don't think he is dead because when MC put the pulse grenade in him, he didn't disintegrate, so he isn't dead.
He fell into a slipspace portal. He is most likely dead though there is a chance the Iso-Didact may return (ANother Didact who fired the Rings)
6. When I watched the trailer, was chief on the arc or planet reach's moon? I think the arc, but other people say reach's moon.
It's The Ark and that is the widely accepted theory; the mountains look similar to Halo 3 and the moon in the background does look like the core. If it took 2 months to build a Ring, it's not unbeievable to believe the Ark has been nearly repaired.
7. When will the war on Sanghelios end? What will the result be at the end? Will humanity get involved?
It ended before Halo 4. The Sangheili Civil War was in 2553, Halo 4 is 2557. Humanity sent the Infinity on a test run to help the Arbiter. 8. What will happen with the arbiter and rtas? Will they meet up with chief? Will any of them die?
I hope they do not, and I doubt they will. Arby and The Chief never really liked each other, just fought together.
9. I know this is off and all, but where is the spirit of fire? From what I have read, it is only MIA, but from 2553. Halo 4 was in 2557.
MIA. It is unkown if 343 ever intend to tell their story or not.
10. The flood. Are they gone for good or are they just dormant somewhere on another planet?
For various reasons, the Big Birdy in the trailer is believed to be Mendicant Bias, who is said to only return with knowledge of how to defeat the flood when it is needed. If he's back, the Flood are.
11. Another off one, but the precursors? Are there any left? I know the gravemind said he was the last one, but maybe they are in a different galaxy.
THe Precursors fled the galaxy, the one who survived the Forerunner's genocide. However (Silentium spoilers)
12. The forerunners. Are they all gone? Just like the precursors thing above, are they in another galaxy building up a fleet to go to war with humanity?
There is a possibility that there are still forerunners still out there, on shield worlds, slipspace bubbles etc. This is not out of the question, but unlikely.
13. This is a really off one, but is there another form of humans on another planet?
No. All the ancient humans were composed into Prometheans, the only species that survived is the one that has the UNSC. Us.
14. Reach. In the epilogue of reach, there is clearly a ship that landed on reach by noble six's helmet. From what I understand, reach was only two thirds glassed. Will humanity re-expand out to reach?
Most likely, The UNSC terraformed Reach as early as 2582 and was recolonising. THis is a possibility, though it will not be a major factor for a long time.
15. Rings. Will the next installment have anything to do with another ring?
I doubt it. Beta, Gamma etc will probably be mentioned but ot would be too much like CE/2 to do again. Best to stick to the plenty of unexplored locations in the Universe for now.
16. The covenant. Will they get any new species maybe? Will any old ones return? Here did the buggers go?
No. The Covenant are a minor player in the story now, the 'Reclaimer' Trilogy is focusing more on the Forerunners. As much as I would love to see this, the Storm, remember, is just a remnant, it has nowhere near the power of the original empire.
17. Brutes. Will they return?
Same as above, ther are nearly extinct through war with themselves and other species. They are still around but most likely won't be a major faction.
18. New species. Will there be any new alien races that are not in the covenant or whatever and just start a war with humanity?
Boring, repetitive and unoriginal. Humanity roughly controlled half the galaxy, and the Covenant controlled around most of the other half. I doubt there is any major space-faring species left undiscovered now.
Hope this helps!