4:10 Heart berry gives a permanent HP buff to one party member. Just +1 max HP, but it's something

5:35 if you don't want to learn the cooking mechanics then you should probably take off hard mode. If you can't optimize your inventory with actually good items then Hard Mode will probably be too hard. Hard mode expects you to actually be able to prepare for fights, not walk in with 5 honey drops and a berry juice. I'm just warning you, if you don't care about the game's deeper mechanics at all and just want to rush the main story quest, Hard mode is not for you. (Well, I guess you could buy pre-cooked leaf omelettes and glazed honeys from the factory gift shop for the entire game, and maybe squeak by on that. Not sure if that's even faster than cooking them when you factor in going all the way back there, though. Certainly costs more berries)

15:40, yes, the whole desert is a sandbox. That is indeed what they're implying.