About the playing and sing at the same time thing....
You have to consider his biggest influence: T. Bone Walker
T. Bone was a blues man in a jazz man's world. You could say he was the first cross-over artist.
At the time (40's to early 50's) Big Band was the popular music. T. Bone was the front man or a large jazz orchestra. Just like Benny Goodman and Tony Dorsey. This is the music that B.B. listen to as he was growing up--as well as the delta blues that was all around his community.
T. Bone's stlye was to sing a little and play a little. Single note phrases and sparse chords while the orchastra kept things going.
So from very ealy on B.B. imitated the same stlye, and he also learned horn solos on his guitar.
B.B. didn't want to be a "traditonal" bluesman. One man one guitar. So, unlike John Lee Hooker who mostly played solo in his early days and made his guitar and feet sound like a whole band because he was the whole band, B.B. King has always had a full band behind him piano, horns and everything just like his hero.
And that's how he changed the face of blues, earned he place in music history and amassed legions or fans. By taking what T. Bone Walker started and mixing in the sounds of the delta and the new "boogie" beat, he brought a never before heard broader sound to the blues, ushered in the modern era, and changed to role of the guitar in blues from strickly rythmic to melodic. So what if he doesn't play and sing at the same time. That doesn't diminish his talent.
James Taylor sing and plays at the same time but he isn't known for his blistering soulful inspiring world changing guitar breaks.
Buddy Guy once said " everybody thats come along since has tried to sound like B.B. King."
If you don't beleive me, spend some time listening to blues just before B.B. Kings arrival and to the music after.