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.

You may be able to install a garbage disposal on your own, especially if you're handy or have some experience with plumbing. However, if you have any concerns or want to make absolutely sure that the connections are installed correctly, you may be better off hiring a local garbage disposal installer to do the job. 

If the cost of repairing a leaking garbage disposal is close to the cost of replacing the disposal, then fixing the unit might not make sense. When deciding if you should repair or replace your garbage disposal, consider the age of your garbage disposal, the cost of the repair, and whether your garbage disposal has had other problems recently to help you decide if the cost of repairing the leak is better than the cost of replacing the disposal.

The main issue with garbage disposals is clogging. This can mean a clogging of the pipes that expel the food along with water, or a clogging of the mechanical parts themselves. The problem lies in the solution because you can’t easily see clogs if they’re inside the system, and reaching in to dislodge stuck items is a risky proposal. Call a pro and ask what they would do, but if you can’t see the clog easily, and running the unit won’t free it, you need to let a professional handle the fix.