To answer your 1st question
How did Doffy get that Flare-Flare Fruit?
just like Kaz Rodgers said
Doflamingo was a black market dealer so naturally his connections probably ended up finding it.
2nd, three of your questions together:
until now I am still confused how the Devil Fruits spread around the world
Do they grow in the same tree or each of them has their own tree (Flare-Flare Tree maybe)?
After the users died, will the fruit grow in the same tree or just fall to random places like Dragon Balls?
For starters, 2. and 3. we don't know much about Devil Fruits either, besides what we have told so far and seen. For example:
- When a Devil Fruit user dies, their ability is reborn into another Fruit of the same kind. Instead of growing from a plant, the ability simply regenerates inside another existing Fruit
As seen when Smiley "died" and the Sara Sara no Mi, Model: Axolotl transplanted itself into a nearby apple.
BUT Oda has pointed out in SBS Volume 48
"For more detail, you'll just have to wait for a certain professor to make his appearance in the story, and explain exactly what the Devil Fruits REALLY are... eventually."