Problem solving and rehearsal

There are two main kinds of practicing I do: problem solving and rehearsal.

The first is working through things I cannot yet play and learning to play them.  One problem is that I do not know what the notes are yet, that I have figured out, on the page, what they are in the literal sense. A second problem is that I cannot get my fingers to play those notes. I have small hands to reach is an issue for me.  

Rehearsing is playing something I can already play, as beautifully as I can. That should be done with intention each time, with thought, never just running through the notes just to refresh your memory.  When I do that, I have to stop myself.  Rehearsal can be experimental... what would be piece sound like a little slower, with a slightly different feel to it, or some other way? Or it can be oriented toward determining one particular interpretation. The interpretation blossoms as I rehearse. It expands or deepens. It can grow stale through excessive repetition. I am not good enough yet to be wholly consistent. Instead, I let the interpretation vary a good deal from day to day, even when moving in a single overall direction. The idea would be to have a single interpretation that only varies a slight bit, but never getting stale either. I am playing the C minor Prelude by Chopin now, which would be easy to play stalely, since it is overplayed, but to me it is fresh (since I'm still at the problem solving stage with it).  

Since I am new to the process, having learned these things just now (this is just what I understand so far), the growth or blossoming in my understanding of the process itself is amazing to me. It is like a strange gift that I don't quite understand yet. It's a bit like discovering a hidden room in a house you have lived in your whole life.  

Recently I was able to hear a phrase in my head before I played and then play it, listening to whether it was the same phrase that I wanted to hear. I'm sure all very good musicians already do that!