6) Vaccines do not necessarily protect against infectious diseases

If enough of a virus or bacteria get into a body no immune system, vaccinated or natural, will prevent it from taking hold. Vaccines have been shown to greatly reduce a persons chance of getting sick, because people only infect other people when they are sick (or infected with the disease) and most diseases need to live and grow in people the disease has nowhere to go and dies out. This is what is called herd immunity.
My understanding is that in addition to herd immunity, that being vaccinated increases your personal ability to fight off the virus or bacteria (so not get the disease at all) OR if you do get it your body has a head start in dealing with the disease (through seeing the antigens of the virus/bacteria via vaccination) and therefore you will get a milder version. [This is all based on the theory that the vaccine contains the strain to which you are exposed and your body creates an immune response to it]. Herd immunity is the second line of defence.