The license terms for Audacity can be found here: http://www.audacityteam.org/about/license/
Audacity may be downloaded free of charge via the Audacity website: http://www.audacityteam.org/download/
No registration is required and we don't collect any data so I don't think we have a privacy document about downloads other than the above.
The Audacity application (as supplied via the Audacity website) does not include any adware or spyware, though we cannot guarantee what third party sites do, so we strongly advise that you and your students always download via the official website. The full source code is available from GitHub: https://github.com/audacity/audacity
Audacity is widely used in schools in the UK, the US and many other countries.