Regarding relaxation, I can explain some of the perspective offered by techniques like the Alexander Technique and the Feldenkrais Method. I have advanced training in the Feldenkrais Method and have taken many Alexander lessons.
There is a difference between learning to relax while at rest, and learning to change your concept of movement so that every movement has less tension associated with it. The former can be very good and can help improve your technique, but the latter can be a more revolutionary experience.
Let me explain this a little more. According to my understanding of the brain, before you make a movement, at a deep level you imagine it. You have something called a self-image, which is a program of how your body works. When you need to make a movement, say moving your arm to the left end of the keyboard, your brain uses this self-image to construct some concept of how to carry out this movement---which muscles to activate, and how to coordinate them.
For most people, the self-image (or the concept of how to carry out a movement) has inefficiencies. It includes unnecessary tightening. The good news is that the self-image can change. You can improve your self-image so that there is less unnecessary tension built into the movement.
I can't describe succinctly here all aspects of how to go about improving the self-image. That's a large topic which is addressed when you take Feldenkrais or Alexander lessons. There are many facets to this.
There is one simple thing you can start to practice, however. A lot of athletes do this. Practice imagining movement. For instance, instead of playing a piece, imagine that you are playing it. You could go through the entire piece, or just pick a few notes from it. Then see if you can imagine the movement getting easier and easier until, in your imagination, it is effortless. Then actually play the part you just imagined, and notice carefully any changes in your experience of it. If you do notice changes, try not to "intellectualize" the changes--- that is, try not to explain them to yourself or "understand" them--- try instead to let them be automatic. Trust your unconscious mind with this.
Try also to include your entire body in your imagination. perhaps you don't usually pay much attention to your lower back. If you need to make the movement in actuality a few times to get a sense of how your lower back feels, then do that. Include all the parts of your that you usually don't notice.