If it's made by dwarves, we call it dwarven. If it's made by elves, we call it elven. Just because it's called Dwarven Plate does not mean it's made only for dwarves.
For magic items (which is what Dwarven Plate is), page 140 of the DMG states;
In most cases, a magic item that's meant to be worn can fit a creature regardless of size or build. Many magic garments are made to be easily adjustable, or they magically adjust themselves to the wearer.
Rare exceptions exist. If the story suggests a good reason for an item to fit only creatures of a certain size or shape, you can rule that it doesn't adjust. For example, armor made by the drow might fit elves only. Dwarves might make items usable only by dwarf-sized and dwarf-shaped characters.
And as Quentin states, for general rules on armour there's page 144 of the PHB;
In most campaigns, you can use or wear any equipment that you find on your adventures, within the bounds of common sense. For example, a burly half-orc won't fit in a halfling’s leather armor, and a gnome would be swallowed up in a cloud giant’s elegant robe.
The DM can impose more realism. For example, a suit of plate armor made for one human might not fit another one without significant alterations, and a guard’s uniform might be visibly ill-fitting when an adventurer tries to wear it as a disguise.
There's also nothing in the item's description that restricts it to only dwarven characters. Unlike the Dwarven Thrower which specifically says it needs to be attuned to a dwarf.
So, as a general rule, whether found or custom made, (within reason) it can be worn by any race.
It's then up to you to decide what limitations/realism you add to it I.E if it's found, does it auto adjust to fit non-dwarves or would they have to find someone to adjust it for them, are the dwarves actually willing to make this very rare magical armour for other races without good reason.
One thing to remember though is be consistent. If you put restrictions on one piece of armour (magical or not) you should also apply restrictions to others.
Another thing to consider is to ask the other players (and DM if you're not DMing) what level of immersion they want.
Do they want to simply be able to wear any armour they come across or do they want that extra bit of realism that makes them drag their loot half way across the country to find someone willing the make the necessary adjustments.
Does Armor Stack?
In general, there are two notations for AC:
The most common variety sets your AC to a fixed value, and looks something like this:
AC = 11 + Dex Modifier (Padded armor)
Your AC equals 10 + your Dexterity modifier + your Wisdom modifier (Monk Unarmored Defense class feature)
Alternately, some items increase your existing AC, and look more like this:
Wielding a shield increases your Armor Class by 2 (shield)
... You gain a +1 bonus to AC (Fighter Defense fighting style)
When calculating your AC, you get ONE item of the first kind, and as many of the second kind as you can justify (except where contradicted by rules for specific items, e.g. you can only use one shield).
So if you have a Dragon sorcerer/barbarian, in full plate, with an extra set of padded armor under it, you have to pick which of the four forms of AC you use (Draconic Resilience, Unarmored Defense, Plate armor, or Padded armor). They do not stack.
But if you strap on a shield, that will stack because it grants +2 AC instead of setting your AC to a value. You can even strap on a cloak of resistance for another +1 AC.
See also:
What can I wear with Plate?
The rules state that plate armor consists of the following:
A suit of plate includes gauntlets, heavy leather boots, a visored helmet, and thick layers of padding underneath the armor.
There are no rules for substituting one piece of armor for another (e.g. a helm for a crown).
With that said, it is typically traditional to allow replacement of peripheral items (such as gloves, helms, boots, and bracers).
Best Answer
Yes*.
While none of the rulebooks come out and explicitly say you are allowed to wear robes over your armor (although it may be more realistic to wear your armor over your robes from a practical standpoint), there is circumstantial evidence to support it.
So, even if you don't buy the argument that armor and robes are not the same kind of item (even though they clearly aren't, despite covering the body in largely a similar fashion), the rules provide for the possibility that they can still be combined if your DM chooses to allow it.
Olorin's answer provides further evidence that this is a valid approach to your particular situation, and references a statement of opinion given by one of 5th Edition's lead designers: Mike Mearls. It is important to note, however, that the official arbiter of the rules-as-written is Jeremy Crawford. While the words of Mearls carry significant weight, they are still merely his personal opinion on how the game works at his table.
*The Standard Caveat: D&D 5th edition empowers the DM in ways that 3rd, 3.5, and 4th did not. While rule zero has always applied, 5th Edition chooses not to explicitly codify many things. If your DM says you can't, you can't.