Ebook reader: open file (and the overall problem with closed source, dumbed-down app ecosystem)
I found a partial answer to my overall problem, and a good solution to manage my ebook collection.  

The key was to go back to the sources of the Spirit of Open Source software. I installed F-Droid: https://f-droid.org/  a catalogue of FOSS (Free and Open Source Software) applications for the Android platform. Browsing the repository, I found some good ebook readers, including 'Cool Reader' which fairly deserves its name. The good thing is that there is an embedded file browser, so that I can now easily browse and open my collection of ebooks that I copied over from my computer to the external sdcard.  

Overall, I found that the problem is the messy ecosystem of closed source, dumbed-down applications found at Google Play. From now on, F-Droid will be my first source when looking for applications for specific needs. In the best tradition of Open Source software, the applications there will certainly evolve into solutions that are friendly both to the newbies, the average users and the power users.