The Olympians are unaware that Olympus is a living sentient being that was born from a young girl's soul who was murdered on the top of Mt Olympus and was slumbering deep in the mountain when they claimed Mt Olympus as their home. The young earth bound spirit grew stronger over the Millenia by absorbing the magical and emotional residue that the Olympians generated over time.
Olympus is the combination of the gods powers as such she is a true daughter of the gods and has inherited some of the powers and abilities of the various gods that reside in her territory.
There are only two members of the Olympian's massive family that are aware of the existence of Olympus, those two being Hestia the goddess of the hearth who Olympus views as a mother and Great mother Rhea.
Despite Olympus' age and Celestial powers when it comes to her ghostly abilities she is quite weak as she has depended on the foreign energy of the gods instead of ectoplasm to survive.
Olympus cannot really recall her mortal life.
Olympus has a huge attraction to Danny Phantom due to being able to see his memories and the feeling of home he brings with his ecto energy.
Danny has no idea who this beautiful girl is and why she haunts his dreams but he does know that he can feel her sadness and her need for help if only he could hear her.
Danny is far more powerful than anyone truly knows this is due to him not unleashing his awakened true form.
The reason Danny does not unleash his true form is due to the consequences it would bring as to do it would merge his mortal and ghost halves together forever.
Danny is unique in that he has two haunts: his natural haunt he got when he became a ghost and the haunt he inherited when he became the ghost king.
When Danny inherited pariahs keep Danny decided to change it up and embrace his love for space and sci fi and scoured the internet for the best designs and transformed into Phantom city a place where Danny welcomes all and protects all.
Danny is worshipped but none more so then Blobs and Wisps two of the very low class Ghost that Danny decided to give their own subservient haunt in his Ghost-Zone haunt as well as any other ghost. This is accomplished when the doors that the ghost use in the Ghost-Zones are attached to a building in the colony creating parent child relationship between the two it benefits the weaker ghost for not only the protection but by combining their doorway to a building it creates a bigger pocket dimension then what the ghost could create on their own.
Danny's two realms are unique as Danny can travel to both of his realms by using the inner sanctum . The inner sanctum is similar to the pocket dimension of the doors in the Ghost-Zone and only Danny can access it.
Danny also uses his Ghost-Zone haunt to try relieve the stress and boredom ghosts suffer from in the zone by creating a coliseum and various other places of entertainment.
The ritual to turn Danny into the ghost king was unpleasant as his heart and ghost core were fused to the heart of the Ghost-Zone which not only stabilized the Ghost-Zone but it also heals the Ghost-Zone.
Danny 's true ghost core isn't an ice core no it's a Pulsar core or a living core created by the merging of the ghost half core and his human heart creating the strongest core of all.
Although chronologically still a young adult Danny doesn't know that through all his time travel adventures he's actually a couple of thousands of years old this is due to the fact when Danny assists Clockwork he wears clockwork medallion that not only allows him to step through time but also stops his own aging.
Dani/Ellie is very much Danny's daughter no matter what others say and after he rescued her from the GIW he was never going to let his baby girl go.
The cure/stabilizer that Danny gave Dani was not a permanent solution and after the rescue from GIW Danny consulted Clockwork who said the permanent fix was to de-age her so that her body was more accepting of the changes. And Danny is completely fine with it as his little 4 year old princess is now the center of his world.