Here's an answer to your question:
1. Regarding DNA being unique to each person:
The only exception to this is identical twins
Hower, the twins' fingerprints will be different because of minute environmental differences. This is how twins can be distinguished by criminologists.
2. In organ transplants, it's important for the recipient to take their anti-rejection drugs on a regular schedule. However, rejection can still occur, because the recipient's immune system cannot be completely suppressed.
The only organ that can be transplanted without concern over rejection is the cornea (part of the eye.) The cornea does not contain blood vessels and receives oxygen by diffusion from the air. If the cornea had blood flow, it would also be susceptible to rejection.
3. In blood transfusions, the blood is filtered for white blood cells to prevent a transfusion reaction. White blood cells are active in the immune system and would be too likely to cause a reaction even though the antigen and Rh types are a perfect match.
DNA is found in the nucleus of each cell, but with no white cells left in the blood, you only have platelets and red blood cells. Platelets are not full cells. Red Blood Cells happen to be the only cell in the human body that do not
have a nucleus. Since RBC's don't have nuclei, they don't carry DNA.
Therefore, when a donor's blood mixes with a recipient's, there's no donor DNA in the person's bloodstream.
I wrote this information before I looked for a link. Turns out I'm exactly right!
I'm a nursing student, formerly pre-med, and hematology (study of the blood) is one of my favorite subjects.