It’s not my place to comment here, but I think that both of your problems is all due to your sites using reCaptcha v2.0: where CF7 now apparently uses reCaptcha 3.0, ..
With the one at “seitenstopper.de/kontakt” asking to fill in a “I’m not a Robot [x]” click box, ..
‘The message could not be sent. Please confirm “I’m not a robot” and click on SEND again, or try again later. Or inform the administrator of the website.’
But there’s no box to tick.
My fix: I had to delete all of the version 2.0 plugins before I could get CF7 forms to send the contact mails correctly.
As I say: it’s not my place to comment, but what’s being reported here as an error with the plugin, (isn’t), but it’s also an issue that I went through before I got the forms to work properly. There’s also a lot of u-Tube vids out there on this issue.
Hope it helps.