I heard from a friend that if nothing covers the bowl or plate of food, there is a direct radiation affect on the food you eat. Is that true?
Many plastics used in the kitchen are unsuitable for use in contact with hot food, whether wrapping it or sagging onto it when used as a cover. Freezer bags are a relevant example. These may melt, or leach into the food. I don't worry about this as much as I probably should; some people are very cautious.
A sealed wrap is also a bad idea, as it can burst under steam pressure. For example leaving a bag clipped shut. This is rare though, and also applies to an unvented cover of cling film.
A loose or vented cover is a good idea for keeping the microwave clean.
Microwave radiation isn't blocked by anything you'd use as a microwave cover/wrap, because then your food wouldn't heat up. So it's a good thing your friend's cover does nothing. Microwave radiation is blocked by metal, including the mesh in the door. The emission of microwaves stops instantly when you open the door, because we're made of meat and would cook quite easily (plus the WiFi would be jammed).
All links are from Wikipedia and are further reading for the curious.