Yes, at http://nemo.sonar.codehaus.org. It regularly analyses some open source projects.
Sonar analyses Java projects, even if they are not built with Maven (more details). Some plugins support other languages like PHP or PL/SQL.
No, Sonar is a standalone web application. This infrastructure is more flexible and powerful but needs an application server and a database.
This may be addressed by Maven reports like dashboard or xradar.