Learn Russian: Алло! Кто это?

Алло is used almost exclusively when answering the telephone. If you were greeting someone face-to-face, you would use Привет (informal) or Здравствуйте (formal), but on the phone, Алло is the standard way to say 'Hello'.

Where is the word for 'is' in Кто это?

In Russian, the present tense of the verb 'to be' (am, is, are) is almost always skipped. Because of this rule, instead of saying 'Who is this?', Russian simply says 'Who this?' (Кто это?).

Could I say Что это? instead of Кто это? in this situation?

No, because Кто means 'Who' and is used for living beings like people and animals. Что means 'What' and is used for inanimate objects. Since you are asking about a person on the phone, you must use Кто.