My mom's appendix ruptured and her body became infected. Since then she had congestive heart failure, chronic kidney failure, can it all be connected?

Yes. When an appendix ruptures, there is risk of sepsis. Sepsis can stress the heart and kidneys resulting in heart failure and kidney failure respectively.
Yes, although rare. A ruptured appendix can cause bacteria to invade the blood, called septicemia. The bacterial toxins in the blood can lead to inflammation that temporarily damages blood vessels. This can lead to shock and a drop in blood pressure, which may cause damage to the heart, lungs, brain, kidneys, and liver. These effects are usually not permanent unless one has pre-existing chronic medical problems.