Maybe at a higher rank, but at a lower level they are essentials 100%.
No no no it's even more prominent at lower ranks because high ranks can usually make do out of a situation with what they are given. For one, the biggest error I see is "lower sensitivity results in higher accuracy." This is absolutely not true, it is whatever you feel most comfortable with that results in higher accuracy. Some of the most accurate players to ever play the game competitively used high sensitivity and DPI set ups.
"Don't challenge an AWP if he knows you are there", again, highly situational. Challenging the AWP could possibly win you the round. If they are covering a site, smoke them off and push them to a chokepoint, or pop flash in and rush him. Both are a near guaranteed kill if your cards are played right, it secures you an AWP, and puts you 1 man up.
"CZ-75 is your best pal on eco rounds" again, situational. Sometimes buying an MP7 or nova is a much better bet. Consider the economy of the enemy team, if you think it is bad enough to where they might not get armor, buy a nova, or if you think they don't have head armor, buy an MP7. They give more money per round and gets you closer to buying an AWP for your team.
"Buy armor on pistol rounds" waste of money and easily countered, buy a better pistol and some flashes or smoke, it opens up more strategic options for your team, is better than a straight up rush, and will equip you to deal with armored opponents.
"If you have the bomb don't yolo off alone" This is good advice most of the time, but if you get a read of the enemies strategy, sometimes a fake and a plant at the opposite site can be a really good strategy, especially on eco rounds (for either side).
"Never buy a gun if you can't afford armor" *Never buy a rifle if you can't afford armor. Buying a shotgun without armor is a perfectly fine strategy, especially on eco rounds when you have a bit of spending money unlike your team.
"An eco round is when your team doesn't spend money" An eco round is where your team spends minimal money to assure you can all buy rifles, armor, nades at the same time. It doesn't mean don't spend any money. In fact it is encouraged to get yourself a p250 or cz if you're low, or a five-seven, deagle or shotty if you're higher up in cash.
"Don't run and gun unless using an SMG" If it is fairly close up range, you're better off staying mobile and spraying rather than stopping or stutter stepping. Especially if they have a shotgun.
As for HLTV, it is only a reference, numbers can be deceptive. The only true way to get accurate good bets, is to watch each teams individual performance and take notes of their strengths and weaknesses.
Good tips though, just need tweaking.