Yes.

The actual rules for this are oddly worded, but the notation is pretty simple.

In general, there are two formats for "things that increase your AC." The most common format is the one attached to armor:

[your AC equals] 11 + Dex modifier

or Draconic Resilience:

your AC equals 13 + your Dexterity modifier.

Note that there is no "plus" at the beginning of the formula. These items set your AC to a specific value.

The other format is that used by shields and class features that increase your AC above its base value:

Defensive fighting style:

You gain a +1 bonus to AC.

Or a shield:

Wielding a shield increases your AC by 2.

These are phrased in terms of increasing, rather than setting your AC. They are preceded by the phrase "increases" or a plus sign.

So, it's pretty simple. You get one thing that sets your AC, and any number of things that modify it (except where restricted by other rules, like the rules stating you can only use one shield).

A fighter could very easily have an AC like this:

[15 + Dex Mod] (half-plate) [+2] (shield) [+1] (defensive fighting style)

For a total AC of 18 + Dex Mod.

But he couldn't add a chain shirt to increase his AC, because both that and the half-plate set his AC to a fixed value.

The same applies to Draconic Resilience. You can stack it with a shield, because a shield increases AC. And you can further stack on the Shield spell, giving you a (temporary) total of [13 + Dex Mod] [+2] [+5], or 20 + Dex Mod.

But you can't combine Draconic Resilience with Mage Armor, because both Mage Armor and Draconic Resilience are trying to set your AC to a fixed value.

Some things Draconic Resilience stacks with:

• Shields

• Shield spell

Some things it does not:

• Plate

• Mage Armor spell

• Barbarian Unarmored Defense class feature

RAW

The rules for AC are on page 14 of the Player's Handbook, or page 9 of the Basic Rules.

The relevant part is this:

Without armor or a shield, your character’s AC equals 10 + his or her Dexterity modifier. If your character wears armor, carries a shield, or both, calculate your AC using the rules in chapter 5. Record your AC on your character sheet.

[...]

Some spells and class features give you a different way to calculate your AC. If you have multiple features that give you different ways to calculate your AC, you choose which one to use.

The rules called out above appear to be these:

Wielding a shield increases your Armor Class by 2. You can benefit from only one shield at a time.

If you wear light armor, you add your Dexterity modifier to the base number from your armor type to determine your Armor Class.

(and so on, for each type of armor)

The rules are sloppy here. Technically, they don't give you a calculation for AC when wielding a shield and no armor. And they never explicitly call out what is or is not a "way to calculate your AC."

With that said, we can use examples to build the intent of the designers.

It's pretty clear that you don't have to choose between a shield and plate. It's also pretty clear that a shield shouldn't set your AC to 2.

Finally, it's pretty clear that wearing a chain shirt with half plate shouldn't set your AC to 28 + 2 * Dex modifier (max 2).

It seems obvious then, that a "calculation" is something that sets your AC to a value plus other modifiers.

If something just adds on to (or increases) your AC, you continue to use whichever calculation is most favorable plus the new modifier.

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.