Is there radiation in space

Yes, a ton of it. Radiation isn't necessarily a ton of plutonium floating around emitting radiation and it's not a cloud of green gas hovering around the moon. It's most common form is a gamma ray, which is a very high energy photon (a light particle.) Gamma radiation, X-ray radiation, and microwave radiation are all light waves that are invisible to the eye, but strong enough to cause damage to cells. The source of this radiation could be stars or other large-scale chemical and nuclear reactions (Quasars, Pulsars, Black Holes, etc.) In fact, the heat of the sun could be considered radiation! It mostly stems from infrared light waves! The sun also emits neutrons to some degree.

The majority of this radiation gets reflected by Earth's magnetic field, and a lot of it can be absorbed/reflected by a ship's shield (aka the Space Shuttle's outer paint and hull materials.)

Other sources of radiation could be in fact radioactive materials left over from these reactions or items activated (made radioactive) by interactions from outside radiation. Typically, the radioactive materials encountered in space would be in the form of ionized molecules. If they are unstable (number of electrons differ from number of protons by a large amount,) they could emit various particles, including beta radiation (electrons,) and possible alpha particles (basically a helium ion with no electrons.)

So, to summarize, yes.