Yeah, the Djinn use shapeshifting for disguise and deception. They are "the Hidden Ones" and exist alongside us in this world, doing whatever it is they can do to spurn us because they don't particularly like us.
They're shapeshifting should have the ability to disguise themselves as other people or living things. Or, you could forgo shapeshifting and just go with the power of Glamours to represent potent illusions. One thing I would do if making one of the djinn, though, would be give them the Gaseous Form power to represent their true state as beings of smokeless fire. Instead of gas, obviously, you'd be a glowing, fiery energy being, but the effect is the same.
For magic I would stick with Spirit Channeling to keep the cost down, perhaps make it Self-Sponsored. Spirit is "smokeless fire" so it seems most apt.
I'm not sure how to do wish granting... Glamours? Sponsored debt? Thaumaturgy?
You can do it just about any way you can think of. It depends on how you want to do it.