To pull something off, is an idiom, and English idioms often do not make sense when you look at the individual parts, it is a term that just means what we have agreed to. I do not know the origin of the idiom, but I can give you a picture. Imagine a bottle with a top on it. As much as they all have tried, all of the adults in the room cannot seem to pull the top off of the bottle. A five year old comes into the room, sees what everyone's doing, walks over to the bottle and pulls the top off. Everyone says "How did you pull that off?" I used this example for two reasons, first there is a direct linkage between the first and third definitions you listed above. Second, it actually provides the usual circumstances surrounding the use of the term. When you "pull something off" you achieve something that either no one else seemed able to do or that people never expected you, specifically, to be able to accomplish. You achieved the unachievable.

pull off Informal To perform in spite of difficulties or obstacles; bring off: They pulled off a last-minute victory.

I have some bad news for you... it's otherwise and you really do have to learn them by rote. Sorry, we call these expressions idioms and the meanings are completely different from the regular meaning. Every language has its idioms, they add wonderful color to the language which is a part of the culture just like the fashions, food and the music. Good luck!