A friend's daughter downloaded US$400+ worth of apps! He'd to try to get refund for each of them.
All glares from screens are bad for eyesight. In fact, the bigger the screen, the further the eyes should be.
Phone radiation is also more harmful to young children than adults due to their thin skull. So yes, switch to airplane mode and turn off Wifi.
I let my 2-Yr old meddle a little with my iPod Touch once in a while, as a last resort when I run out of distractions, especially outdoors. I store many nursery rhymes inside, so he listens to the songs instead of playing with apps.