I would recommend looking over the school's specific requirements for the SOP. Usually they ask what to talk about, and if not you can email the graduate coordinator if there are any specific things to talk about. Most of the time they want you to discuss why you have an interest in the field, and a short personal story to explain your rising interest would be appropriate. If written correctly, it can show your motivation and drive for the area of interest.
For your second point, I would again look at their requirements. Ask the program coordinator if it is appropriate to write about a specific lab/professor. For my programs, it is absolutely essential and if you don't your SOP will likely be thrown in the trash. It shows that you've looked into why this program is right for you and where you would fit best.
For the last point I don't think I have much guidance due to my unfamiliarity with your field of study.