No not all eggs have or contain Salmonella.
The eggs that do get salmonella get infected when the chicken who lays the eggs has been infected with Salmonella.
If the chicken who laid the eggs was not infected with Salmonella then there's no chance or way that the eggs would be infected with Salmonella.
Only a small percentage of eggs contain Salmonella which true for chicken as well.
However when you do cook the chicken or eggs all the way through at a high enough temperature then the Salmonella will be killed off.
Salmonella cannot survive when it is heated to high temperatures during the cooking or baking process.
So as long as you cook the chicken or eggs all the way then you should not get infected with Salmonella.