How kann I avoid a redirect after submiting a form and show the success message? Seems to be unusual, cause I haven't found much info about it.
ChronoForms doesn't do anything after the form is submitted unless you add action(s) under the submit tab.
Under Basic actions there is a "Message" action that displays a message.
Under Basic actions there is a "Redirect" action where you can specify a url to redirect to.
It sounds like you may need to delete the Redirect action and add a Message action.
Including a screen capture in your question might help diagnose the problem.