In Tyranny of Dragons, do the effects common to all Dragon Masks stack if you attune to more than one?

Question

In the Tyranny of Dragons storyline, do the effects common to all Dragon Masks stack if you attune to more than one?

I'm specifically interested in Draconic Majesty, but would like answers for all of the properties below. Let us assume that the character in question will find a way to wear more than one mask at a time, somehow, if necessary.

The dragon masks' properties are described in this supplement for Rise of Tiamat:

Dragon Mask Properties

Each dragon mask is a legendary wondrous item that reshapes to fit the face and head of a wearer attuned to it. While you are wearing any dragon mask and attuned to it, you gain the following benefits.

Damage Absorption. You have resistance against the mask’s damage type. If you already have resistance to that damage type from another source, you instead have immunity to that damage type. If you already have immunity to that damage type from another source, whenever you are subjected to damage of that type, you take none of that damage and regain a number of hit points equal to half the damage dealt of that type.

Draconic Majesty. While you are wearing no armor, you can add your Charisma bonus to your Armor Class.

Dragon Breath. If you have a breath weapon that requires rest to recharge, it gains a recharge of 6.

Dragon Sight. You gain darkvision out to 60 feet, or to an additional 60 feet if you already have that sense. Once per day, you can gain blindsight out to 30 feet for 5 minutes.

Dragon Tongue. You can speak and understand Draconic. You also have advantage on any Charisma check you make against dragons that share the mask’s color.

Legendary Resistance (1/Day). If you fail a saving throw, you can choose to succeed instead.

Answer 1

No, but also Yes.

First, I'd like to point out the rules on wearing multiple items of the same kind:

Use common sense to determine whether more than one of a given kind of magic item can be worn.

A mask that "reshapes to fit the face and head of a wearer" sounds like a textbook example of an item where you can only wear one at a time, but I'll assume, as you state, that you have two heads, or some other way to wear two of these masks.

Even if you can physically wear both masks, magical effects with the same name don't stack, per the DMG Errata:

when two or more game features have the same name, only the effects of one of them -the most potent one-apply while the durations of the effects overlap.

Since abilities like Draconic Majesty and Dragon Sight are "game features with the same name", they don't normally stack.

None of this applies to the Dragon Masks in particular, since they have their own stacking rules described in the Rise of Tiamat book, on page 94:

If you try to "assemble" multiple dragon masks, they become the Mask of the Dragon Queen, and give you the properties of exactly one mask at a time, while giving extra Damage Absorption and Legendary Resistance.