The Bene Gesserit control people by knowing how to modulate their voice to trigger people’s base instincts. Like, that instinct that tells you to run when you hear a tiger’s roar, or shiver when you hear a whisper. It’s just that, cranked up to 11. Iirc, they can only really use the Voice on a person after having studied them to find what they will react to (or if they happen to be particularly weak-willed).
As for seeing the future: Computers were replaced with humans long ago in Dune, but they continued to fill and develop those niches with the human mind. Future-sight is essentially like a supercomputer running a simulation, which is why Paul is able to see the future better when he takes spice, or the Water of Life. By gaining the latent genetic knowledge of his ancestors and thereby having more data to work from, he is better able to run these mental simulations.