George Harrison's soundtrack to the film Wonderwall was the first official solo album by one of the Beatles. I think it was late 1968.
As to who is actually credited with breaking the group up...I'd have to say it probably started with George, who was starting to become a good songwriter, but John and Paul would only toss him crumbs, a song per album. I think George was the first Beatle to actually take a break from the group for a while, (Ringo, too). But John was the first to officially announce he was leaving the group, around Sept. 69.
The Chuck Berry song was "You Can't Catch Me", and the first line in "Come Together" is almost identical to Berry's. Obviously, John was paying tribute to Berry. But I think it was Berry's music publisher, who owned the rights to Chuck Berry's songs, that brought the lawsuit. Ka-ching!