The sun is practically a massive nuclear fusion reactor which kicks out a ton of radiation. So naturally there's going to be more ambient radiation, we have a layer of our atmosphere I think which deflects a lot of harmful radiation. Also if I'm not mistaken, the sun occasionally kicks out a high levels of radiation every so often which is deadly to humans, the crew of the ISS have shielded areas they can go to when this happens.
So yes, there's lots of radiation in space, more so than on Earth.
And the (ionizing) radiation is mainly high energy rays - X-rays, Gamma rays and cosmic rays.
The radiation that we typically think of as harmful (e.g. from Radon, Uranium) is "particle" radiation - Alpha and Beta, both of which are easily stopped by a layer or two of paper, but are very harmful when we breathe in or ingest (eat) radioactive elements, which then release radiation directly into the body.
TBH I think that the inclusion of the Android (conveniently, erm, left out of the MR summary) and iPhone is a cheap attempt to get some media/popular interest in the NASA programme - I'm sure that all of these experiments could have been done better with an Atmel AVR, TI OMAP or Altera eval board and some sensors. But whatever. The application for these apps sounds rather contrived.
"The three-axis gyroscopes and accelerometers in the iPhone 4 are expected to perform very well in zero-gravity, and are being tested as an alternative to much more expensive equipment."
Presumably made by STM or an handful of others. Yeah, using COTS equipment is much cheaper than space-qualified parts. And modern MEMS technology is cheaper than a laser gyro... Can I go work for NASA now?
Meh, at least it's not *my* tax money.
PS FWIW I think we should colonise Mars.