Non-mortal magic is what comes out of things like demons, fairies, gods and a few mythical creatures. It is different from mortal magic in several significant ways:
Players can get access to POWERS, as this magic is called, in several ways. Having a demonic or divine parent is one, as is possessing faery blood. The chances of my allowing this route are becoming increasingly slim. Gods and demons (the distinctions between these two classes of immortal can be a little blurry) can both "grant" powers to a mortal, though dealing with either can be tricky unless you really know what you're doing. Magical items incorporating the essence of an immortal will allow access to some or all of the being's powers, usually without too much risk once the critter is safely trapped.
Demons are divided into as many different sorts as are mundane creatures, and are sometimes indistinguishable from their mortal counterparts. Some are non-corporeal, some are shape-changers, still others have fixed forms. The level of intelligence among demons ranges from virtually non- existent right up to supra-genius, and the physical form of a demon is not necessarily any indication of it's mental abilities. The only things which all demons can be said to have in common are an innate magical ability (of variable power), and an absolute disregard for mortals, especially intelligent mortals, except as playthings. Some of the more sapient types gather together in organized societies under leaders known collectively as the Demon Princes, and these sorts tend to have less contact with humanity than solitary demons. They are certainly the most dangerous ones to summon, since you are liable to get a whole bunch of them turning up to offer their Summoned cousin immoral support.... in which case you had damn well better have some way to appease, amuse or dominate them.
There is no connection between the Demon Lands and the normal mortal afterlife, but it is possible to end up there by annoying the wrong people. There is such a connection, however, between the Demon Lands and the Dreamlands, where it is possible to make contact with demonkind without summoning them into the world. Contrary to popular opinion, most demons can enter the world under their own steam without too many problems, but they can't usually be bothered. They can be kept out though, if you know how.
The reason that demons are of interest to mortal magicians is that they can be "tapped" for their magical powers. This can be voluntary, in the form of a permanent or temporary transfer of power by the demon, or it can be involuntary when the wizard traps the demon in an enchanted object with the purpose of accessing its abilities. A voluntary grant should always be viewed with extreme caution, as demons are not normally known for their philanthropy.
"Fairies" is the collective term for a huge range of elves, dwarves, sprites, spriggans, goblins, banshees, imps, gnomes, ogres, sylphs, dryads, pixies, kobolds, brownies, satyrs, etc. etc.
The number of fairy forms is as numerous as fairies themselves; like demons they need not necessarily be of any fixed form, or have any physical body at all. Unlike demons, they are native to the world and are more comprehensible to mortals - indeed, they share many of the same emotional attributes as us, notably greed, vanity, curiosity, sentimentality, cruelty, spitefulness and lust. They can be generally divided into two groups: the Light and the Dark. This nomenclature has nothing to do with how late they stay up at night, but is more to do with Good Guys and Bad Guys.... though it is true that the Dark tends to prefer the dark. On the other hand, so do many of the Light, and things can easily get a little confusing. The two sides are enemies and always will be, but that doesn't mean that each side doesn't have its internecine squabbles as well. And though some types of fairies tend toward one side or the other, it would be a mistake to assume (for example) that an elf was allied to the Light, just because most elves are. Fairy politics is a convoluted and prickly subject, best avoided by anyone who isn't a fairy.
As well as being a magical bunch, most fairy species have in common a fear of and vulnerability to iron or steel...they use metals like copper or bronze for preference. Notable exceptions are the gnomes and dwarves, who are quite happy playing with lumps of steel and do so at every opportunity. It is probably no coincidence that these two races have the least magic of all the fairy tribes.
The attitudes of fairy-folk to mortals is varied, but the most common attitude is one of suspicious contempt. They consider us (as a species) to be coarse and vulgar, brutish and uncultured. But from time to time they will adopt cordial relations with individuals, and in the case of dwarves and gnomes, will sometimes even trade with mortals on more-or-less equal terms.
As far as wizards are concerned, fairies are the most reliable source of magical knowledge around. They are not necessarily a generous lot, but most of them take their obligations seriously, and they will sometimes trade knowledge or magical doo-dads for something which takes their fancy. Bear in mind, though, that many of them are chronic practical jokers and are likely to attach eels to your nose or give you frog's feet if you give them any excuse. (Elves are more restrained than most in this line, and dwarves or gnomes don't have the magical facility for it.)
There is not a lot that needs to be said about gods. People worship them for any number of reasons, and sometimes gain some benefit from it. Most gods have little to do with the world or its inhabitants, but some are intimately connected with a place...these genii loci are the gods which are most often worshipped; they are venerated, supplicated, placated or a combination of the three. Gods have many features in common with demons, but whether they belong to the same species is a matter for (mostly pointless) debate. They are not generally of much use to magicians, but occasionally interfere in the lives of Heroes (seldom to the ultimate benefit of the poor schmuck who gets to play patsy).
This is really hot territory for your magical types. Bits and pieces of any number of endangered species are bunged into soups, stews and potions by wizards trying to gain access to their multitudinous powers, and sometimes with success. Dragons' blood is traditionally good for understanding the speech of birds and beasts, and a gorgon's head is the ideal thing for a garden-gnome business. The basic problem, of course, is obtaining the appropriate bits without being turned into dog-meat oneself..... this is where Heroes come in very handy, since they are generally easily talked into performing potentially suicidal feats on behalf of a smooth-tongued wizard who knows which buttons to push. And they are in reasonably plentiful supply, unlike the poor critters they are sent out to slaughter.
Any self-respecting wizard will own at least one Bestiary jam-packed with exciting pictures of unusual creatures, and informative essays on how to make use of them. (Jane's' "All the World's Monsters", for example). And well-preserved lumps of stuff can usually be relied on to bring in some cash if you don't have any use for them yourself.