The configuration and functionality is currently lacking

1) The help text under the Static Analysis Tool configuration (Freestyle job), should add that the own configured Parser can be found if "Groovy Parser" is selected

For each static analysis tool a dedicated parser will be used to read the report files. If your tool is not yet supported then you can create your own parser in the system configuration.

2) Groovy Parser cant scan console log output ?!
Seems a bit weird to me that a single scanner has this limitation, is this getting fixed, or is there a recommendation to start writing logs to a file first? (As in best practices, generally for Jenkins or specific to this plugin). like using "2>&1 | tee some.log" on commands?

FATAL: Static analysis tool Groovy Parser cannot scan console log output, please define a file pattern