Several questions regarding the writing of SoP
I think your overarching question is "What do I include in a statement of purpose for US PhD applications". You can find several great answers to that question if you search this forum. Further there are many, many sample SoPs available online. If you review previous forum answers as well as sample SoPs, you will be able to answer these very specific questions on your own.

And please do have a native English speaker proofread your SoP, your CV, and all other application material before you submit.