The Tasmanian Devil is a carnivorous marsupial of the order Dasyuromorphia.

The Tasmanian Devil is a carnivorous marsupial (dasyurid) of the order Dasyuromorphia.

Numbats are mammals, and marsupials. They are the only surviving members of their family Myrmecobiidae. This family is one of three that belong to the order Dasyuromorphia (Dasyurids) which are the carnivorous marsupials.

Presumably the term 'tiger cat' refers to the quoll found in Australia. If so, then the quoll and the numbat are more closely related than the numbat and the bandicoot. Both the quoll and the numbat are dasyurids, or carnivorous and/or insectivorous marsupials, being members of the order Dasyuromorphia. The bandicoot is an omnivorous marsupial which belongs to the order Peramelemorphia.

No. The bandicoot and the numbat are completely different animals. Although they are both marsupials, the numbat is a member of the order Dasyuromorphia, while the bandicoot is a member of the order Peramelemorphia.