If Dragon DID eat a Devil fruit, it's probably the Ame Ame no Mi (Rain Rain Fruit). Before you flame me, there's a reason for this, and it's based on the Chinese Emperors of the 5 directions. The four cardinal emperors were:
1. Byakko the White Tiger (Whitebeard), Associated with West and Autumn; a protector, and known as the King of animals and lord of mountains.
2. Suzaku the Red Phoenix (Shanks), Associated with the South and Summer; associated with Good fortune and Prosperity.
3. Seiryu the Blue-green Dragon (?????), Associated with East and Spring; a symbol of justice and benevolent rule.
4. Genbu the Black Turtle (?????), Emperor of Winter and the North, Bringer of Wisdom and Longevity.
Now, in Chinese Myth, there's a fifth, Quan Long, the father of Seiryu. He taught the other four gods knowledge and writing, and had the power to create and control rains. He could also see the future (being 2000 years old, he achieved ultimate wisdom). He taught this skill to Genbu after Genbu achieved 1000 years of age.
In Japan, Quan Long is known as Ouryu, or Dragon King. In addition to their abilities in the Chinese Myth, they can assume the form of humans. They are said to wear a dragon or serpent-like hood, or carry a serpent-like tail. They also are seemingly able to come and go with the wind, spreading their prophecies.
It's up to you if you believe this or not.
As for the time thing, if they train during that time, they get stronger. If they don't train, they weaken. Simple as that. Look at Arlong. He WAS nearly equal to Jimbei. When Luffy got to him, he was still strong, but sucked at combat.
Just to add something and correct some stuff…
Here are some mistakes that you listed. Suzaku is not a phoenix, although in many different adaptations Suzaku has been viewed as a phoenix. Suzaku is actually a bird, a vermillion/red bird. The phoenix is Ho-ou the king of birds (hence the usage of Hou as phoenix) Suzaku being a phoenix is actually a common misconception.
Your description and name "Quang Long" is also incorrect. His name is Qilin
and in the japanese counterpart Kirin. Kirin has always been depicted as a beast with a dragon's head, and an ox like body. Eventually he had become depicted as a giraffe, that's why the word "kirin" is used for giraffe in japan. He is the father of all animals. I don't know a lot about Qilin, but there is another thing to add. He has been considered both as the most fearsome and most benevolent of all the beasts. He is said to be able to walk on grass without crushing on any blade and walk on water. (yes, just like jesus) He does not eat meat, and he is said to breath fire.
Genbu, Seiryuu, Byakku, and Suzaku are all the japanese names for the 4 benovlent animals that you mentioned
The chinese names are the following
Xuán Wǔ: Black Tortoise -to add on Black Tortoise has been mentioned as a 2 headed tortoise, one with the head of a turtle and the other with the head of a serpent.
Zhū Què: Vermilion Bird
Qīng Lóng: Azure Dragon
Bái Hǔ: White Tiger