I love The Grateful Dead, the American rock band.
What kind of song do they sing?
A variety of them! Fom eclectic style, which fused elements of rock, psychedelia, experimental music, modal jazz, country, folk, bluegrass, blues, to reggae, and space rock, 
Who is their producer?
Their founding member, Jerry Garcia is also their producer.
When did they come to lime light?
Around 1965, when they were ranked 57th by "Rolling Stone" magazine in its The Greatest Artists of All Time issue.