Is there a name for the genre that mixes Rap, R&B, Rock, and Pop together (in the style of Vanilla Ice, Lil Wayne, Metallica, and Michael Jackson... ), all in one song?
Are there significant artists working in that genre?
The fusion of rap and rock is called, pretty predictably, "rap-rock." Some of the better known artists who work primarily in that style are Rage Against the Machine, Limp Bizkit and Kid Rock.
The fusion of hip-hop and R&B represents a large percentage of contemporary black American music (see my answer to this question), so much so that it doesn't make sense to pick out individual artists.
For artists who are known for combining that entire range of different styles with a pop sensibility, you might try Outkast (Bombs Over Baghdad), Janelle Monae, Red Hot Chili Peppers, the Offspring, Beck, the Roots (The Seed 2.0), Mary J. Blige, Frank Ocean, Beyonce and Kanye West.