SEO homepage and other crucial pages

The search performance for the homepage is disastrous. For example it doesn't seem to rank for the keyword "amp" at all. For other more specific keywords its behaviour is also quite strange:

That's the SERP for "amp framework" in an anonymous session for me for example. For other keywords there is a proper result for the homepage but not with the title or description the page provides but something that has been picked by the Crawler. My guess is that both our maintained title and description are too long.