I just got done with a re-read of the journal and I took notes here are some possible conclusions I have found:
- Jun did die on Reach, right after Jun and Dr. Halsley boarded the pelican, she was taken to a camp where John was being held at. There, she briefed John on what he next mission is but, before this happen John was taken to the underground lab inorder to run a few more tests on John to update the Mark V armor. So there, Jun decided to stay and fight but the rest of Noble did not know of his death.
-The original Hasley is probably dead but, she did clone herself with more than one copy so, one of the clones is probably still alive.
-There is kinda another Cortana. In the journal she talked about how she split Cortana in two. Part for her and part for John, that's why they have always had a close relationship.
- If Jorge didn't die before them picking up the package, it would have been Jorge that stayed with her and not Jun. The reason for that is Jorge was handpicked by Dr. Halsley and she watched him the most other than John.
-Jorge was the only real Spartan on the team. All the others were Spartan III's and were not trained by the UNSC but a special program created by ONI and they didn't even use true Spartan Armor but just something that was used by ONI, that's why they don't look like true Halo Armor in Reach.
-Finally, they had health shields, but they shouldn't have had those shields. The reason was, she couldn't find a strong enough power source for the shields to be powered until right befored she left the planet.
Those are my theories and if you have any others please add.