The student intro rate is $20/month and includes everything. That is for the first year only and requires a one year commitment.
Short answer: Yes, InDesign is included with the Creative Cloud. There are Desktop and Mobile apps. Some applications that are not included are:
CC Desktop Apps (with subscription)
CC Mobile Apps (with subscription)
Students and Teachers can also pre-pay for 1-year and get a discount to $199: Creative Cloud pricing and membership plans | Adobe Creative Cloud