The quick answer is: (1) yes, (2) both and (3) as long as your definition of "science fiction" isn't too particular. The world of Dragon Ball is full of high technology, most notably the convenient pocket-sized capsules (as seen in the trailer) which pop open into motorcycles, houses, guns or what have you. Several of the heroes and villains are aliens or cyborgs, and one of the major storylines involves a journey to another planet on a spaceship which takes several months to arrive at its destination. At the same time, the series also has magic, witches, demons, fortune tellers, gods and scenes set in the afterlife. And a high-level hero or villain has enough ki power to blow up the entire planet.
The long answer is, Dragon Ball was originally intended as a sort of Fractured Fairy Tale, a play on the Chinese legend Saiyûki (Journey to the West). (The same legend used as source material for the 2007 Monkey: Journey to the West stage musical and Jamie Hewlett's 2008 animation sequence, Gene Yang's graphic novel American Born Chinese, the 1978 Monkey TV series, Kazuya Minekura's bishonen manga Saiyuki and much more.) Although his personality and appearance are quite different, Goku is loosely based on the Monkey King; that's why he has a monkey's tail, a magic staff and rides around on a cloud. (Most of these elements are jettisoned in Dragonball: Evolution.) Toriyama also added to the mix a large dose of Hong Kong martial arts movies, particularly Jackie Chan's Drunken Master. Toriyama has even said that Jackie Chan in his youth would have been the ideal person to play Goku.
The celestial bureaucracy of the Dragon Ball universe, in which there are several layers of by no means omnipotent "gods" in charge of the earth and the universe, is also vaguely reminiscent of Chinese mythology, although no comparisons to any real-world religion are intended. When asked about his world's religion in the January 2003 issue of SHONEN JUMP, Toriyama replied "To be honest, I wasn't really thinking about it too deeply."
The other big influence in Dragon Ball is science fiction. Toriyama is a fan of sci-fi movies (his favorite is Alien), and Dr. Slump is full of gags based on Star Trek, Star Wars and other sci-fi and monster movies, not to mention plenty of fanciful cars, hovercrafts and dinosaurs. In fact, the Chinese style of Dragon Ball was originally intended as a break from Dr. Slump's Western sci-fi themes. But over the long course of Dragon Ball the story loosened up and acquired more and more science fiction influences. Gamera has a cameo in the series, as does a thinly disguised Arnold Schwarznegger from The Terminator, and Freeza, one of the villains, transforms into a creature clearly based on H.R. Giger's Alien. Dr. Slump and Dragon Ball even take place in the same universe-the Dr. Slump characters appear in a lengthy cameo in Dragon Ball volume 8.
The clearest point at which Dragon Ball turns from mythology to sci-fi is the shocking revelation which opens the Dragon Ball Z part of the storyline-in which Goku, previously just a weird kid with a monkey's tail, is revealed to be one of the Saiyans, a race of mercenary space aliens. Of course, this was all made up retroactively, as Toriyama himself admits; originally Goku was just supposed to be like the Monkey King. Did we mention that in Dragon Ball, the gods are aliens too?