I can sing "Share my voice" in original version but it is stressing. If I sing it comfortably, I sing it in A instead of Eb. My vocal range starts from D2. So up to now I often transpose exercises except I wish to train mixed voice and falsetto.

It works, but wouldn`t it be nice to have a few templates made for Basso-Singers?

Hi, Karsten! My beginner course uses a different song with a limited range called "Shake it up" in the key of Bb. I sing it in the range of G3 to G4, and it should be comfortable for you down the octave (G2 to G3)! 

Also check out this video I did on easy songs for beginners: the video description has songs for each voice type, and you can see if any non-bass songs would be a good fit for you in a lower octave. Songs in the alto range should be an easy fit, for instance!

Finally, see this article on low voice types with a list of basses for you to listen to and learn songs from!