Children may have an increased risk of adverse health effects from cell phone radiation. According to American Academy of Pediatrics President Dr. Robert Block, when cell phones are used by children, "the average RF energy deposition is two times higher in the brain and 10 times higher in the bone marrow of the skull," than for adults.  A July 2008 peer-reviewed study shows that children under the age of eight absorb twice the amount of radiation into their brain tissue as adults due to their lower skull thickness. 
Depends on if you have other sources present in your home as well. Cordless home phone+base station, Smart Meter, Non-eco Wifi-Router (Eco will reduce the 10 pulses to 1 pulse per second on your Router, even when it has no connected devices.) An ethernetcable will work great, but make sure to disable the active wifi connection on your Laptop or Pc.
The company's "Researches" page, for example, states that "Aires Technologies are more than 12 years (sic). For this period there have been conducted a number of studies on mechanisms of coherent transformers that effect on physical, chemical, technological and biological processes (sic). The studies were carried out in close collaboration with leading research and academic institutions."
The answer is yes, it can. Will it always make people sick? No. Dr. George Carlo explains that there is most definitely a biological response to what he refers to as Information Carrying Radio Waves (ICRW-energy fields from many wireless devices). When you're exposed to ICRW a process of adaptation and compensation occurs in your body. He has a great program that can help people adapt.
Cell phone storage in front pockets has been linked to poor fertility and higher chances of miscarriage and childhood cancer.  According to the Cleveland Clinic Center for Reproductive Medicine, semen quality "tended to decline as daily cell phone use increased."  According to a May-June 2012 meta-study in the Journal of Andrology, "men using mobile phones have decreased sperm concentration" in addition to "decreased viability" of their sperm. 
Cancer is the obvious start. An early concern with mobile technology was clusters of the disease around those living near phone masts. One study in Israel found a 4.5-fold increase in cancers of all kinds in the immediate vicinity of a mast (Int. J. Cancer Prev., 2004). In 2009, a Korean team of researchers carried out a pool analysis of the results of 23 studies, which involved almost 38,000 subjects.