Try to put some angle on your highbacks, it will force you to a lower position and bent knees which will help when riding on bumpy terrain. Also if you find rollers (shaped like ~~~) try to practice there. Bend your knees over the bumps and extend between. Try to keep your upper body in a straight line and you legs working. Straightlining through rollers is a great exercice to get your riding more dynamic.
As for the ice some speed might actually help you since you wont slide out and fall. Try to look for buildt up snowpiles on the ice, aim for them and make your turn there. Also keep your edges sharp.
Carving on steeper hills is a challenge, in the beginning try to make a C shaped turn, in the beginning and end of your turn your board will be traversing across the hill. This will keep the speed down which is important at the beginning, as you progress try to ride more down the fallline as you get more comfortable with the speed. Riding fast is also a lot in your head, you need some mental toughness to be relaxed at high speed so take it in small steps and dont try to race everyone else. Ride just outside of your comforzone all the time.