Can you become immune to sepsis?

No. Many different bacterial, viruses, fungi, etc... Can cause sepsis, an overwhelming infection spread throughout the body. Most of the germs that can cause sepsis are not vaccine-preventable.
Depends... There are 2 vaccines given in infancy, which can greatly decrease an infant's risk of sepsis due to 1) pneumococcus and 2) hemophilus inf type b bacteria. Make sure your baby gets these vaccines, and gets them on time. The last cases i saw of these types of sepsis were during my hospital training, as the vaccines were being introduced to the public, many years ago! the bacteria are still out there.