Thank you for your quick reply.
SSL is configured by me. I have no other issues with it.
I checked the certificate with digicert and there is no problem. Everything is green.
I want to remind you what I wrote in first post:
In AutotweetNG Free (latest version) options I use:
Routing mode: Exmperimental (it's the only one that gives my the right SEF urls)
Enable URL routing: ON
Validate Url: No
My ONLY problem is that when I push the "publish" button to post a new article (in article manager) it doesn't return me to the right url /administrator/index.php?option=com_content&view=articles but to a wrong url /administrator/component/content/?view=articles.