No, you do not need a garbage disposal to have a dishwasher. A dishwasher will work without one, and while it's rare to see a home with a dishwasher that doesn't have a disposal, it is possible. The two appliances pair well and are often installed together because a disposal simplifies meal cleanup.

However, your dishwasher should not be used as a replacement for a garbage disposal. Subjecting it to continuous food leftovers can lead to major clogs. If you choose not to install a garbage disposal, you should thoroughly rinse your plates or scrape excess food into the trash or a compost pile before loading them into the dishwasher to prevent plumbing issues.

There are many maintenance and repair issues that lead to a malfunctioning garbage disposal. Regular clogs place wear and tear on the motors, leading to an eventual shutdown. Electrical issues at the breaker, wall outlet, or disposal itself can fry the unit. The most common cause is simply a worn-down motor. These motors can only handle so much use before powering down for good. 

Whether it's worth repairing your garbage disposal depends on its age and the specific problem. Generally, if the unit is eight years old or younger, repair is a good option. For minor issues like a bad seal or a simple jam, a repair can be inexpensive, sometimes under $10. However, if the motor is broken (a repair that can cost $150 or more) or the unit is getting old, it's often more cost-effective to replace the entire disposal.

Your garbage disposal will only affect the health of your septic tank if you’re using it too frequently, or filling it with organic waste that doesn’t fully break down. If the tank fills up with too many solids, the bacteria won’t have enough time to consume it before more is added, which can lead to an overflow in the drain field. Your tank will need to be pumped more frequently with excessive or improper garbage disposal use.