I disagree with a lot of these sayings. The first one about being good enough to play then good enough to raise is nonsense to me. There are many times you will have mid pocket pairs like 55-88 and they are good to call with a set mine but you wouldnt want to 3 bet with them (especially in pots that are pre ante in tournaments as an example). There are multiple other types of hands where overcalling is okay so you would not want to raise or be 3 betting every hand. Limit poker you can make that argument I think to always come in for a raise but that is a whole different conversation in my opinion.
The 3 bet being between 3-5% is also off. This should depend on the game you are in and how often your opponents fold to 3 bets. 3 betting between 3-5% is fine (its actually my 3 bet %) but there is nothing wrong either depending on the game of having your 3 bet % be in the neighborhood of 7%. This would mean you have some 3 bet bluffs in your range which again, depending on opponents, is a good thing. Don't think you have to stay in the range of 3-5% as it will box in your game. If that's where you fall naturally then that is fine but don't strive for that to be your stats.
Third saying is fine but 3 betting can be an effective
bluff against the correct opponents or can lead you to an early exit as well. Depends on the game but again dont get boxed in to thinking it is only for when I want to play a big hand as even though most of the time that is true 3 bet
bluffing (such as when in the SB against a late position raise) can be a very effective tool to use.
Pre flop raising sizes is a personal preference in my book but it should also be somewhat a factor of the game you are in as well. A game that has a lot of 3 betting you want to open smaller and games where there are tons of fish then you can open larger with big hands as they will call down more often. There always seems to be a debate between 2x and 3 raising pre. To me most players who are calling 2x will also call 3x and if they are folding to 3x they will probably fold to 2x. Only exception that I normally see would be the Big blind since they already have a BB in the middle. Think of it though as do we want them calling when we have a raising strength hand and they have any two? I say yes so personally I like smaller pre flop sizings in the neighborhood of 2-2.5x for tournaments. Cash I think should be 3-3.5x for micros (players tend to call more so you can get more value going bigger) and as you get higher stakes should be more in the 2.5x range.