I don't know anything about the science but I can answer part of the medicine.
In this period there were many advances in the knowledge of the human anatomy.
1540, a Belgian physician named Andreas Vesalius started cutting up dead criminals to get a better idea of the human body. By doing this he proved ancient writers, such as Galen, wrong in their beliefs of the body. For example, Galen stated that the human liver has 5 parts, but that is not true. The human liver is actually one part.
Another man, French surgeon Ambroise Pare, made many advancements in surgical operations, particularly in war hospitals. For example, when a man was wounded in battle, and his leg amputated, it was customary to use a red-hot iron to seal the wound. Pare instead tried sew up the cut blood vessels again, and it worked and his patients healed faster.
There were also discoveries such as the fact that the heart is a pump by Dr. William Harvey in 1628.
Hope this helps!
Thoth