You don’t have to store eggs in the fridge; if you have a cool cupboard or pantry (under 20° C) you can keep them in there in a container. This means you won’t have to leave eggs out to get to room temperature for baking.
The easiest way to retrieve bits of broken egg shell when you crack an egg into a bowl, is to use a bigger piece of the egg shell. Simple scoop up the broken bits with the bigger piece of shell and they will stick to it (rather than trying to drag broken fragments up the side of the bowl which can be a little frustrating!).
If you want a fried egg with a runny yolk, drizzle a tablespoon of cold water over your fried egg while it’s cooking to let it cool down. This will extend the cooking time a little, but stops the yolk from drying up before the white is cooked.