Yes.
Yes. A cheetah is a type of feline and felines are cats. You can see this by how they are scientifically classified.
Domain: Eukaryote
Kingdom: Anamalia
Phylum: Chordata
Class: Mammalia
Order: Carnivora
Family: Felidae
Genus: Acinonyx
Species: A. Jubatus
The family they are in, Felidae, is the family for cats. You can see from reading this: http://en.wikipedia.org/wiki/Felidae
Yes! Cheetahs and cats may appear different in size or even their fur, but they are both of the same family.
Yes .