I have a question about the procedure of the flow validation.
When I submit my form and then flow shows a validation error for example for the url input field without deleting all the already inserted user inputs from the fields.
How does flow keep the field filled out? Which methods / classes are involved? Is there a way I can influence / copy this behaviour?
By default your controller extends \TYPO3\Flow\Mvc\Controller\ActionController, and by default in case there are validation errors errorAction() from this controller is called. Inside there is forwardToReferringRequest() just read the code to get it.
If you want to change this behaviour you can override errorAction() in your controller (same as any other protected/public method). You can also change $errorMethodName and handle it using different action on your controller level. Check this example https://wiki.typo3.org/Flow_Cookbook#handling_validation_errors_that_occur