It looks like your MacBook's hard drive is bad. You can't partition the drive, you can't load the MacOS, and no matter what you try, you can't get it to boot. Must be a bad hard drive right? So you go out and buy a new hard drive, install it, and guess what? Same problems. Now what can you do?
Replace the hard drive cable. Many different MacBooks have hard drive cables / ribbons that fail sometimes. Your problem may not be a hard drive at all. Hard drive cables for MacBooks are not too expensive but it seems like every different MacBook needs a different cable. Be sure to order the right cable, or let a professional install a new cable in your MacBook.