I will assume by "derby" you mean Kentucky Derby. I will also assume that you only mean winners of the Derby. There have been two Derby-winning horses with 15 letters in their names: Foolish Pleasure (1975) and Fusaichi Pegasus (2000).
Big Brown
both i won once in the derby
The Kentucky Derby didn't begin until 1875.
No. The horse can be any color as long as they train and are ready. I believe there are more brown horses than black horses thet enter a derby.
Thoroughbred horses compete in the Kentucky Derby.
Thoroughbreds
both
both
Twenty horses can race at a time
Not in the Derby.
The Kentucky Derby
For horses, the Derby in America, known as the Kentucky Derby, is run in Louisville, Kentucky, on the first Saturday in May every year.