And about turning the game off when it says "game saved" but before actually starting the day, I really hope that's true! That would help solve a lot!
That's where you're Supposed to turn off the game. But you're already saved, you can only start the new day when you turn on your game.
Restarts means to power off or reboot your game in the middle of gameplay.
To fix store inventory, you have to buy/ship something then play through the game and sleep-save. Check the next time the store is open.