No; undercoats are for protection against water or cold weather. Retrievers have an undercoat because they were bred to retrieve game from water. Huskies have an undercoat to help them stay warm in very cold climates. Lots of other breeds have undercoats.
Breeds like Dalmatians and Great Danes don't have an undercoat.
If your dog has an undercoat, it's important to brush its coat regularly to avoid matting. Dogs with and without undercoats shed, some lots, others not so much, with the exception of a few breeds like Poodles.
No, not all dogs with fur have undercoats. Some of these dogs are Great Danes as well as Dalmatians. There is a breed of dogs that have undercoats such as Huskies as well as Retrievers; it is acts like their protector against cold weather.