What an excellent set of questions:
There is a digested list of what has changed in each release in the release notes: http://docs.moodle.org/dev/Moodle_2.5_release_notes
That always contains a link to the full list of changes in the tracker: https://tracker.moodle.org/secure/IssueNavigator!executeAdvanced.jspa?jqlQuery=project+%3D+mdl+AND+resolution+%3D+fixed+AND+fixVersion+in+%28%222.5%22%29+ORDER+BY+priority+DESC&runQuery=true&clear=true but unless you are very patient, a list of 718 issues is pretty useless. You can download those issues in various forms using the 'Views' menu in the top right.
Moodle provides demo.moodle.net (running the latest stable version, currently 2.5.1+) and qa.moodle.net (running the latest development version, 2.6 dev or master) where you can always try out the latest functionality.
Before each major release, there is a big effort to get people to help with testing Moodle. See http://docs.moodle.org/dev/QA_testing. That uses this list of testcases: https://tracker.moodle.org/browse/MDLQA-1. There is also a lot of automated testing, so the list of many test-cases was actually shorter for 2.5 than it was for 2.4.