In my experience faeries live in faery, dragons have their own plane but the weave between all the worlds I think.
My friend has a dragon guide and he seems to be fairly permanent (even pops over to visit me from time to time hehe).
Like faeries, its best to expect nothing and hope for everything lol. I also find that when I meet a new dragon you are very polite to them. Some are old and ancient beings and love to be flattered with pleases and thank yous. Course every now and then you will find a grumpy bugger
I have no experience with dragons myself but my son who's 15 now has been seeing a dragon near him, usually as he's about to fall asleep for around the last 6 or 7 years. It doesn't frighten him - he says it hovers above him and glows a yellowy colour.
Have you thought about reading DJ Conway's book 'Dancing with Dragons' - there is lots of info in there about how to get in touch with dragons and your own dragon guide.
I love dragons, and have been fortunate enough to have somehow attracted the attention of a dragon guide.
There are many different kinds of dragons, and yes, they do have their own plane, although from what I've seen they can manifest on the Astral relatively easily when they so choose. They seem to use that as their interface with humankind, the ones who'll speak to us, that is!
There are dragons who don't particularly care for humans, at all. Those generally avoid us. The ones who do like people are in many cases either very young ones (hatchlings) or older ones who have taken an interest in specific individuals, for reasons of their own.
Dragons are extremely intelligent, and are most of them are excellent mages, even the baby ones. Magic comes naturally to them, and if a dragon decides to teach a human draconic magics, that person is lucky indeed. So far mine hasn't done this. She's protected me, and has steered me away from trouble concerning magic use. But she's not just a guardian, she's a friend first and foremost. I think that's the most important thing.
I think the best way to contact dragonkind is to think very seriously about wanting to meet one. They're telepathic, so if you send out a positive message, don't be surprised if you get a response. It might take a while, though. They're apparently very careful, and check you out before deciding they want to have anything to do with you. I know, sounds snobbish, but they are very different beings from ourselves, and many of them have had unsavoury interactions with humans. Take St George, for example...
This may be why they've decided to take up residence on their own plane, one which is more hospitable to their particular form.