Karpov's advice was to study endgames more. Ulf Andersson said to 'learn chess backwards' i.e. as darkmagegurl says above.
Learning openings is ok if you can already play chess but otherwise you will end up losing a lot of 'won' games. Finally, you can't rely on traps to win chess games. Chess is a game of creative thinking (plus knowledge plus pattern recognition plus technique ....)
The OP's point number 4. is absolutely correct for OTB play though IMO.
I actually think the opening is the most important because 1. It will be easy to make the correct move in an opening you know well and you can punish opponents for not knowing it. 2. By studying the opening, you also learn what the correct plan will be in a particular opening instead of making the wrong plan and lose your advantage. 3. traps are a very easy way to get a won position. 4. all of this will probably keep you out of time trouble since you would know what you are doing.
Next important would be the endgame because you have to know how to actually win your won games or try to save your lost ones. It would really suck if you won the opponents queen but when it's just queen vs. king, you don't know how to do it! Of course it really helps you convert very small advantages or even maybe inferior positions to a win.