Can magic be used without keyblade?
Yes, because otherwise we wouldn't have half the organization being able to cast their signature magic (unless somehow it turns out that they ALL can use/did use Keyblades at some point...)
During Days when Xion was unable to use the Keyblade she was using magic to survive.
But even if we discredit all of the "main" cast and assume they are somehow special: the fact that FF characters can use magic also seems to suggest that "regular" people can also learn to use it. We also have seen Minnie using Holy...so it seems to be that anyone can really use magic if its convenient to the story.
Personally I lean towards the idea that while the presence of magic just varies greatly between worlds (every disney world is obviously going to be different), within the universe as a whole it's just a normal...
thing that anyone could pick up and learn with a little practice, but you would need to actually have training to do so.
Presumably Leon, Aerith, heck maybe even Cloud learned their magic from hanging around Merlin at some point? Minnie could have been taught by Mickey...
I believe that people are born predisposed to magic. (As a hypothetical race to which Sora, Riku, Lea, Cloud, Leon belong)
I mean, we have no reason to believe that Sora is inherently GOOD at magic. His first spell is literally just...handed over to him by Donald and he doesn't seem to express any particular surprise/joy/anything at being suddenly able to
literally set things on fire (but this might have just been limitations at the time) and regardless of how much "training" you do with Merlin, the dialogue at Radient Garden in KH2 seems to suggest that everyone credits Sora's ability with magic at all to Merlin's help. If we are good at it or not kind of depends on the player.
Now, I dunno if regular everyday people are casting spells in their houses but I assume not. From everything we have seen so far it seems, to me anyway, that anyone can learn but you need to actually learn from someone who can actually teach you. I'd be willing to bet that in future installments if Hayner, Pence and Olette hang around the Keyblade gang long enough they will be able to shoot out a few spells of their own at some point.