In this guide, the first step should be to identify which make of drive is currently installed. If it's Seagate, install a Seagate drive. Ditto WD or Hitachi. I have one that's got the Seagate cable and I am putting in a 2TB SSHD and will report back on if I have the fan issue.
Yes, you don't need the specific suction cups to remove the display cover - it's held on by magnets, and if you start at the center by the iSight you can work out to the edges and remove it. I had an iPhone screen suction cup around and it helped with balancing the screen when you pull it out fully, but by no ways is it required.