Yes... if I understand you correctly. Since we are, as God intended when He created us, embodied souls, or ensouled bodies, the body and soul absolutely go together. Together, they constitute “you.”
Nope. My soul and spirit constitute "me". Body is just equipment. Ask Stephen Hawking, spiritually dead to God, but alive in the body. When his soul and (hu)man's spirit depart from his body, he will be physically dead, but his soul will be alive. Does he want that body back again? Maybe not, but that's what he will get if he doesn't heed the call.
Do you not know that Jesus came to save souls, not bodies?
Jesus is able to give the "me" component a new body, minus any remnant of the "old man" in it. That's what I want. (He will have the only damaged body in Heaven. AFIK.)