Hello Tobias,
Thanks for writing in!
To correct the https mismatch, please go to Settings > General and make sure that the site URL, WordPress address URL, and your WP dashboard URL is the same using http or https.
Which demo did you install first? You should be able to see two home pages in Pages. One of the Home pages is for the Church and the other is for the App. You can open each of the pages in Cornerstone and then save it as a template so that it will appear in the template manager. Please check out these knowledgebase articles:
Hope this helps.