Cooking benefits all classes, especially melee and hunters (it is a free source of food). Until higher levels, the benefits it provides are almost exclusively stamina buffs. While more stamina is always nice, cooking is not essential to leveling. Considering the time investment required, if you pick up skinning then cooking would absolutely be a wise skill to level prior to hitting your level cap, as beasts often drop meat useful for skilling up.
Level with a pet if you can because it will help keep you safe. If your pet is tanking all of the damage from the enemies you’re fighting, you won’t have to. The other reason is that pets are easier and cheaper to heal than you are. If you don’t have a pet, make sure you know how to use your defensive abilities. You can’t level quickly if you are dying all the time.
We have no idea what implications this might have and whether or not it even indicates anything, since Patch 8.2 is still in testing and a Tuesday launch is more than unlikely due to Essence tuning and Azshara's Eternal Palace, which is supposedly coming shortly after launch. Blizzard said they wouldn't be delaying the new raid like they did with Battle of Dazar'alor.