So Obito and Kakashi had the ability to warp anything into Kamui time space with their mangekyo sharingan, in the final battle kakashi and Obito went into the Kamui timespace and fought each other. Can kamui be used inside the time space, if so does the object go to real world or different dimension?
Inshort technically it is possible (see 3rd point for exact process)
As I mentioned in my comment not enough information is available as limited use of Kamui was seen only towards the end of the series however following conclusions can be drawn-
Using Kamui is the only way to travel to and from its dimension. This means that targets transferred there are trapped, forced to stay until Kamui's user lets them leave; Obito sometimes uses genjutsu on those he imprisons to keep them subdued.
Obito's two Mangekyō Sharingan spend years with different users – Obito himself and Kakashi Hatake – this makes Obito and Kakashi essentially immune to each other's Kamui:although one of them can use Kamui on the other, the other can just use Kamui on themselves to escape.This also means they can block or counter each other's attempts to use Kamui on others
Kamui ordinarily only connects its dimension with the Earth. If a user synchronises Kamui with another space–time ninjutsu, Kamui can travel to the other ninjutsu's target dimension.(Proof-Naruto chapter 683, pages 14-15) Some technique's similar to Kamui are-
In the anime, the Hizashi Hyūga of Jiraiya Shinobi Handbook: The Tale of Naruto the Hero uses a technique similar to Kamui.
The space-time ninjutsu of Shin Uchiha, Nue, and Kinshiki Ōtsutsuki are similar in function to Kamui.
But if the user doesn't have the original ninjutsu to piggyback off of, travelling between dimensions becomes extremely difficult since Kamui doesn't naturally connect to them. Users can manually generate portals to these other dimensions with Kamui, but this requires a great deal of chakra, so much that users will likely need another person's assistance. Proof-Naruto chapter 685, pages 3-8
Additionally, Obito in the Purgatory is able to use Kamui to temporarily return his soul to Earth to continue assisting Kakashi by granting him the use of his Sharingan for a short time. Source-https://naruto.fandom.com/wiki/Kamui