Have you discussed these things with your teacher?
The e minor Nocturne is quite a gem, I still play it often and I first learned it in 8th grade, although I admit I didn't know what I was doing then. Which Rach Prelude are you doing?
A good place to start, if you know your theory, are with scales that match the key(s) of your rep. There is no point in starting with C Major, then G, D, etc unless you are learning theory, too. In fact, C Major is the most difficult scale to PLAY (but easiest key to READ, so we start with C Major). Don't worry about mixing your articulation, etc, at this point. Learn control with a forte tone for now, then comes speed and variations of the scales. You might as well throw some arpeggios in there, too, of course!
I never let my students (no matter what level) learn an entire piece hands alone unless there are a few spots to work out in one hand. Most of the time, especially in late intermediate music and above, the hands work together, so, for example, you might tackle a fingering in the R.H., only for it to not make sense at all once you get both hands going. Or, you might get some notes and a good tone in a L.H. melody, but once you add R.H. arpeggios, the L.H. gets lost again and you have to start over in a sense anyway. I tell my students that learning entire pieces one hand at a time it like learning a piece three times.
Also, if you HAVE to learn an entire piece hands separately just to get the notes, then the piece you are looking at is too difficult. One of my pet peeves is/are teachers who assign music that is WAY too difficult for their students. The teacher thinks they are "challenging" the student, but the challenge can come from many other channels than simply from a piece where a student can't even get the notes. If you want to challenge a student, give them K.545 and make them play it 5 different ways, yet all be acceptable for the style. Don't give them Bach's First Invention one week and Chopin Etudes the next. Okay, I forgot what my point was, sorry.
Topic: Practice!