Tortoises and turtles, members of clade Testudinata have both internal bones in their legs and head, and an external shell protecting their torso. If I understand correctly, they have both an endoskeleton and an exoskeleton.
A turtle’s “shell” is a carapace and plastron, which is really just an extension of its endoskeleton. There are some extinct classes of jawless fish which also had hardened scales, but as far as I’m aware the turtles (terrapins, tortoises, and true turtles) are the only land-dwelling (or at least land-egg depositing) vertebrates with large skeletal extensions that cover the torso region.
No. The shell is made of bone, although there are thick scales on the outside (called scutes), which is what you see. The bony shell is made up of expanded bones from its back bone and ribs. Turtles are unique among vertebrates in having their shoulder and pelvic girdles located within the rib cage.
Armadillos are mammals. Mammals are the earliest surviving branch of land vertebrates with an amniote egg, that is, above the level of the amphibians. The other surviving branch, Reptilia in the broad sense, includes turtles, crocodilians, lizards, snakes, and birds. So not closely related at all. Certainly the shells of both are evolved independently.
Vertebrates have two different kinds of bone. Endoskeletal or cartilage bone originates from cartilage that becomes converted to bone. The spine, ribs, limbs, and lower jaw are endoskeletal bone. Dermal or membrane bone doesn’t form from cartilage but from within the epidermis. Parts of the skull and shoulder girdle consist of dermal bone. However, dermal bones can also form in the skin to create the shells of armadillos. The shells of turtles include both endoskeletal and dermal bone.
Whether turtles and armadillos have both an endoskeleton and an exoskeleton depends on how exactly you define them. Neither has their actual bones exposed on the outside of the body. The bones are covered by scales that are part of the skin. On the other hand, the shells do form within the skin, the outer layer of the body. But in this sense all vertebrates have both an exo and endoskeleton, since parts of the skull are dermal bone.
This contrasts with the exoskeleton of arthropods, mollusks, and other invertebrates, which is usually exposed on the outside of the body. However, it should be noted that arthropods also have an endoskeleton of sorts, in that the external shell has internal projections that serve as the site of muscle attachment.