Are the insecticides used on the bed nets safe? What are the brand names and chemical names of those insecticides, and can you point me to any studies that have been done to determine their safety?
The short answer is yes, the insecticides used in bednets are safe under the conditions in which people are exposed to them through using bednets.
Most standard bednets are treated with a chemical known as a pyrethroid, and usually permethrin or deltramethrin. Both of these chemicals have low toxicity to most mammals and are poorly absorbed by the skin, making them safe for treating bednets. There are some studies on mice which suggest that pyrethroids such as permethrin can be carcinogens when ingested, though once bound to the fibre of a bednet the chemical is not ingested by the person sleeping under the net so this is not a danger.
The World Health Organisation maintains a comprehensive set of specifications (PDF) for maintaining quality and safety in insecticide treated bednets.
There is another WHO report on the safety of pyrethroids (PDF) for public health use, which gives more details about conditions under which these compounds are considered toxic and the risk of exposure through bednet use.