Club trajectory is severely affected on downhill shots. Take a more lofted club, adjust your weight and chase your swing down the hill
You can putt with your eyes over the ball or slightly inside but never with your eyes outside of the ball, but regardless of how you putt your eye line must match the putter you have so have a club fitter help you select a putter that you are comfortable with
With a traffic cone behind you practice your downswing trying to keep the club inside the cone to simulate the correct approach at impact, this will help eliminate casting, over the top and other downswing faults that create curved shots and an improper impact position