I did the ole' steeple in college...first thing, if you are having trouble with stutter stepping into the barrier make sure you consciously speed up going into the barrier; this will help. I, unfortunately, could never do a full hurdle with either foot forward and this was my trick to getting it right.
Stepping on top of the barriers (excluding the water) will slow you down. Try to hurdle all if you can, if you're in a big crowd you might have to step on top. However, I lost a race because I was very tired at the end and decided to step on the last barrier and was kicked down by a guy who hurdled it.
For practicing the water pit: you don't want to always be practicing it on the actual water pit as it will mess with your legs and ankles...the pit is pretty steep and you don't want to injure yourself. We always placed a barrier at the edge of the long jump pit and practiced jumping out from the barrier and then landing in the soft sand. A few reps of this multiple times per week will help a lot.
For practicing hurdling: make sure you are doing a lot of flexibility exercises and stretching. Don't practice with the actual barrier, because if you clip it or mess up, it's gunna hurt and maybe end your seasons. Practice with regular hurdles that are more forgiving.