Over the summer, JazzHub was opened to the entire software development community.  JazzHub is free for public projects, and currently free for private projects (we anticipate monthly fees for private projects in the future).  The complete terms of use are posted here: https://hub.jazz.net/terms.

JazzHub is a place where you can collaborate with others to seamlessly plan, track, and develop software in the cloud. Visit http://hub.jazz.net/ to get started.

You have done already the most important step on using the Jazz tools by registering for jazz.net. If you want to use tools locally on your machine/network, there is the offering of using Rational Team Concert for up to 10 developers for free. You can find the conditions on the download side (it supports derby as database and Tomcat as app server, both bundled in the download). There are no such other programs for the other Jazz based tools like Requirements Composer or Quality Manager.
If you are an academic user or working on qualified projects, than you are allowed to work with Jazz based products on the Jazz hub -> look for the Academic area on jazz.net.

No parts of the Jazz platform are open source.

Hope that helps.

Also, note that the online development tools at JazzHub are built on Orion (http://www.eclipse.org/orion) and RTC is built on Eclipse, which are both open source.