I've found that for beginning adult riders, getting your heels down is one of the hardest things to get used to. It's just not a natural position for your leg, especially when you're working not to let your lower leg get too far forward. This is not something that comes right away and is so common so do not feel bad! This is something that will definitely come in time. In the meantime, it may be helpful to work on stretching your calves on a step multiple times a day while slightly bending your knees almost like you were riding.
As far as your hands, once you become more balanced, your hands will definitely steady. Concentrate on letting your weight sink into your heels and relaxing your arms as you ride.
Work on the longe line is incredible for helping with balance and really letting you work on your position without having to worry about controlling your horse.
Rest assured that it will get easier as you keep up with your lessons!