There should be some standardized easy to use tools for automating these tests and capture debug information (eg, backtraces and memory dumps) in a format suitable for a bug report in the event of a failure of a test. That should help in providing good quality bug reports for the developers to find the problem and come up with a fix.
as for (2), another set of easy to use scripts can be devised to automate the process of getting the latest sources from git from appropriate developer repos and building the new binary packages appropriate for your distro. Such scripts can be called from the test suite scripts as well when checking for solutions for failures.
Automating bug reporting and solution checking will be a big help for end users and developers alike, so problems can be found and fixed and fixes pushed out to users.
I believe Microsoft does something like this with Windows via the Error Reporting services by prompting the user to send the crash report to MS and also check if there is a fix available. If a fix or workaround for that particular crash is available it's obtained and installed automatically. Linux can benefit from something like this as well.