“I can “pop” my own back” or “my friend just pushes on my back while I lay on the floor”. Is that okay?

No.

Only Chiropractors are trained to detect subluxations (misalignments) and correct them. How do you know which vertebrae needs to move and if it was the one that moved? In most cases when a person has a subluxation, it will make the vertebrae above and below become hypermobile (increase movement) due to the fixated vertebrae in the middle. When you twist/ lean back in a chair to adjust yourself, you are moving the hypermobile segments instead of the subluxated vertebrae. This could speed up degeneration or whatever present damage exist in that area.