[RPG] With starting equipment, do crossbow bolts come with a case, like arrows come with a quiver

I want to challenge your approach to this. As you note, the Light property is defined like this:

Light. A light weapon is small and easy to handle, making it ideal for use when fighting with two weapons.

This property isn't just there as a computer function — it's also part of the basic description. A hand crossbow is small and easy to handle. And it is, as far as crossbows go, ideal for fighting with two weapons. You may need special practice and training (as represented by the feat) to take advantage of it, but it's undeniably better than any other crossbow for that case.

Is it true that mechanically there are no current rules which make particular use of this property? Meh. Probably so. But it does not mean the property shouldn't be there, because that kind of mechanical interaction isn't the only reason weapons have descriptions.

It might have been more elegant from a "the puzzle pieces must fit together!" perspective if Crossbow Expert said "a crossbow with the light property" instead of "hand crossbow", but I don't think that really would add much of actual value.

Of course, there's always the possibility of future features which apply to "light ranged weapons" or the like.

5 weapons is correct if you always choose the option with the most weapons. Though this probably isn't the best use of your initial equipment loadout.

You could list them all on your character sheet, but it might be better to note your attack bonus (your strength mod plus your proficiency bonus plus any other bonuses), and your damage modifier (your strength plus any relevant bonuses), and then either write down or remember the die that you roll depending on which weapon you're using.

This is probably easier than writing the same expression down several times with a different die in each one.

There are only limits on what kind of attack you can take with a specific weapon if specified. One such limitation is for two weapon fighting which requires light weapons.