Correct. Pin 1 and 2 are 12V and GND.
Show Image
(https://i.stack.imgur.com/IA43b.jpg)
They must be soldered to the short and the long prong on the Coaxial plug respectively. Just like in this picture, but the red wire will be yellow in your case.
Show Image
(https://playground.arduino.cc/uploads/Learning/9V_tut_3.jpg)
PSUs have the female molex so that's the one you'll be chopping off.
Show Image
(https://upload.wikimedia.org/wikipedia/commons/thumb/3/31/Molex_female_connector.jpg/220px-Molex_female_connector.jpg)
Double check what's your power plug (https://en.wikipedia.org/wiki/Coaxial_power_connector#Standards) as they are very similar to each other.
You're the man
(https://media.tenor.com/images/b24bb9ff41a82800534691ccb10776d6/tenor.gif)