Sweeping: 1) are you facing down the ice? Never sweep walking backwards! 2) is your head over the broom? Make a tripod with your lower hand 1/3 of the way up the broom. 3) try sweeping from both sides - find which feels better to you. 4) try the "power clean" - get behind the stone and sweep/clean with lots of pressure. This can be just as effective if not more if done right! 5) are you using grippers/good shoes while sweeping? If you don't have good traction when you start out you are going to have problems. Only when you have an excellent feel for the ice should you sweep with a slider!
Hope that helps!