[RPG] At what level are Spell Scrolls used

From the "Your Spellbook" sidebar, page 32 of the Player's Basic Rules (v0.2):

When you find a wizard spell of 1st level or higher, you can add it to your spellbook if it is of a level for which you have spell slots and if you can spare the time to decipher and copy it.

Emphasis mine. Only spells on the Wizard list can be learned in this way. In this area, there is no difference between spells written in a spellbook and spells written on scrolls. The difference is between Wizard spells and non-Wizard spells.

Even if the game allowed you to copy a non-Wizard spell into your spellbook, we have in Preparing and Casting Spells, page 30:

You prepare the list of wizard spells that are available for you to cast. To do so, choose a number of wizard spells from your spellbook equal to your Intelligence modifier + your wizard level (minimum of one spell).

So even if you could write non-Wizard spells in your spellbook, you couldn't prepare them and therefore couldn't cast them.

Further down the same page, you can cast rituals without preparing them, but even there, we have:

You can cast a wizard spell as a ritual if that spell has the ritual tag and you have the spell in your spellbook.

So, you can't copy non-Wizard spells into your spellbook, and even if you could, there's just no way to cast them.

Wizards can't use scrolls that are not on their list either, since we have on page 60 of the DM's Basic Rules:

If the spell is on your class's spell list, you can use an action to read the scroll and cast its spell without having to provide any of the spell's components. Otherwise, the scroll is unintelligible.

As to why this is (from a narrative perspective), every method of spellcasting works differently. For example, the Wizard and the Sorcerer probably have the most similar spell lists, but the Wizard uses magic through painstaking study and preparation, where a sorcerer simply unleashes the power they have within them. So a spell that isn't on the Wizard spell list is probably just impossible to cast using the Wizard method of spellcasting.

From a balance perspective, obviously it would be completely unfair if Wizards had access to every spell in the game.

Yes, the wording does mean that a cleric of the Light Domain gains 'Fireball' as part of the Cleric Spell List; and here's why the wording is different. I hope the following helps explain why

"The following spells are added to the warlock spell list for you," which shows that Fiend patron warlocks have Fireball in their spell lists, and so should be able to use Spell Scrolls of fireball.

The above Warlock phrasing, just as it's phrased for Wizards and other spell casting classes that gain extra spells through means of specialization, is phrased that way because each of those classes have a spell list that they must choose spells from as they level up. They do not inherently know all spells available to a Warlock. So the phrasing in this case means the fireball spell is added to the list of spells he can POTENTIALLY add to his 'Spells Known' list. For intents and purposes, those are now on his Warlock Spell List

Now enter Cleric, and the Paladin; which have very different methods of spell learning.

If you have a domain spell that doesn't appear on the cleric spell list, the spell is nonetheless a cleric spell for you."

It must phrase it like this because Clerics and Paladins do not have to choose what spells they learn as they level. Clerics and Paladins inherently have the knowledge of every spell on their list....because we're awesome like that....and can prepare spells as needed in between long rests. If I wanted to go with cure wounds one day and then give up cure wounds to take Inflict Wounds after a long rest? I can do that freely. I have direct access to every spell available to Clerics. So when I choose Light Domain and it says the Fireball spell that isn't on my class list nonetheless becomes a cleric spell? It's now part of my knowledge of cleric spells (On my list of spells), and thus able to be utilized in scroll form since I now have the knowledge of how 'Fireball' works magically.

The only reason it doesn't say these spells are added to your spell list for you, is because it wouldn't matter in a Cleric or Paladin's case. Any spell that's on our spell list is a spell we can cast should we choose to. Any spell that's on a Warlock/Wizard/Sorcerer spell list, is a spell they can cast only if they chose it from their spell list when gaining levels.