It's not about commercial, but "geschäftsmäßig" which is a way broader term. Any form of doing things in a repititve form can inder some circumstance fall inter it's this includes non-profit work, can contain hobby things, ...

This is correct. Also everyone using GitHub or similar services and uploading code must also have an impressum on their GitHub profiles. It applies to all kinds of web presences.

Commercial offering encompasses "serving ads", "writing promotional articles for own services or third party services". It's rather that you don't need an Impressum if and only if the website is neither directly or indirectly linked with a commercial purpose/gain/strategy.