Because it makes the computer "sick" and not working right. And computer viruses spread, so it's like another word for saying a computer is "sick" and not working right. Viruses can spread computer...
Viruses are called viruses because, like real-world viruses (e.g., influenza and so on), they 'infect' a computer and often spread throughout it by making copies of themselves and making their code...
Yup. In the general sense of the term "virus" (any malware that can be installed on a computer), there are some kinds of malware, usually called downloaders, which can actually download more malware...