The entire concept of radiation and its effects on the human body is incorrect. When Maya is burned and blistered by the "radiation contamination," her skin is blistered and burned in a very short period of time; this is typically only caused by thermal radiation, or direct contact with beta fallout from a nuclear blast, both occurring very shortly after the blast, not many years later. With radiation intense enough to burn her skin like that no human would be able to survive. The doctors say that the bodies of people from space have grown immune to the effects of radiation by filtering the radiation out of the bloodstream. The type of radiation that would cause burns like the burns on Maya is called ionizing radiation and passes directly through the body disrupting and destroying cells. It has nothing to do with circulating throughout the bloodstream.
The director/ script/ story writer seem to be totally unaware of the concept of blood groups. Earlier Clarke had tried to give blood to Anya's second in command, without mentioning a word about blood group, though thankfully the girl had died before the blood can be transfused. Now, Maya's and Jasper's bloods circulate through each other's body without any mention of they having the same blood group or their blood being tested. If their blood group is not the same, both would have been done in the middle of the procedure.