What part of the university is Communication Studies considered part of?

It really depends on the type of institution and type of degree. Since Communication Studies is so inter-disciplinary, it could well be considered part of engineering, architecture, mathematics, sociology or even computer science.

Are there any sub-disciplines of Communication Studies?

Yes, there are currently 9 recognized disciplines. They include: Communication and Technology, Mass Communication, Organizational, Political, Rhetorical, Intercultural-International, Interpersonal-small group, and Health.

What is Communication Studies?

In a university setting: Communication studies is the study of communication. Sometimes it is referred to as the sharing of symbols over distances in space and time.
What types of programs incorporate Communication Studies?

Communication Studies can be found in film, journalism, advertising, public relations, and many more.