There are only 2 that I can whole-heartedly recommend:
Nate Bosch's "The Piano System" and "The Sudnow Method". Do a search for these and make up your mind. They are by far worth the money!
yes of course
Andrae Thomas is arguably the best piano player..
Yes, he i playing the piano, the guitar and the drums. Of course he has a vocal career.
Yes. Of course!
That may depends on your level and you're liking. If you're an intermediate and you like jazz, then go for jazz piano level 1, then on level 2, and so on. Or if you are still a beginner then try the elementary ones.
The keyboard is best known as a piano because of there looks, sound etc.
Well, Beethoven wrote for the piano orchestrally. Schubert wrote for the piano vocally. But possibly the first person to write for the piano truly pianistically was Frederick Chopin. There have been many others, of course, but Chopin was the first really great composer to understand, in your words, the "nature and potential of the piano as an expressive instrument".
singing and piano of course!
The piano notes for "Flower of Scotland" can be played in the key of D major, with the melody primarily using D, G, and A notes. The song has a simple and repetitive melody, making it relatively easy to learn and play on the piano.
Some of My Best Friends Are...The Piano Players was created in 1994.
Bach is best know for playing the piano, or piano forte.
I would recommend Juilliard School in New York as the best school for piano.