When airplane mode is turned on, does the iPhone stop giving off radiation?

There are many kinds of radiation. Which ones are you referring to? Light? Heat? X-Rays?

According to the manual, Airplane mode turns off cellular, wifi, bluetooth, and disables GPS. You can, however, turn the Wifi and Bluetooth back on, even in Airplane mode. Heat and light radiation generated by the iPhone are not affected.

That depends on how technical you want to get. All radios are shut off in airplane mode (is is possible to turn WiFi on while in airplane mode, though), so the radiation one normally associates with cell phones stops being emanated. The phone is still an electronic device and will continue to emanate some RF as well as visible light (when the display is on), which are both technically "radiation".

Why do you ask?

No.