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.
It’s just the usual conflict between rules and narrative that is all over D&D 3.5. In reality, The Crystal Shard, where the forging was first described, was written in 1988, long before the 3.5 rules were written.1
As it turns out, D&D 3.5 is not just poor at emulating all manner of characters from other media (cf. character build for Gandalf in D&D 3.5), it’s also poor at emulating characters even from its own media. The rules of D&D 3.5 just don’t line up as well as most would like with the narratives that the rulebooks and novels suggest they go with. If you follow the rules strictly and allow them to dictate the narrative setting, what you end up with is the Tippyverse, or maybe Eberron if you include an arbitrary level cap and deus ex machina dragons to keep things in line.
It is a common criticism of Forgotten Realms, for instance, that it has all these epic-level mages holing away in towers doing apparently nothing (because, by the rules, they could solve pretty much any and all problems with barely any effort, because Epic Spellcasting is broken). This is necessary to have a game since it’s not much fun to run to the nearest sympathetic archmage and have them fix it with a wave of their hand, but it causes conflict between the rules and the narrative.
The narrative-rules interactions also have problems in the reverse: the ranger class is largely supposed to let you play as Drizzt Do’Urden, but since he was a bit of a Marty Stu kind of character who could do everything, the ranger class gets a bit of everything at a drastically cut-down rate, and ends up being quite poor at doing any of those things.
So basically, what Bruenor did is not something players can do by the rules. As Ruut mentions, there are ways to create magic items without casting “spells,” and there are ways of upgrading special magic items you already have, but Bruenor wouldn’t have had those.
It is worth noting, however, that while Player’s Guide to Faerûn gives his class levels, more books were published after that time. In particular, Races of Stone was printed well after that point. It includes a battlesmith prestige class, which was likely an attempt to provide a class that could be used by Bruenor or someone like him to produce magic weapons like Aegis-fang.
- In fact, not only was this prior to Wizards of the Coast, who wrote 3.5 in 2003, acquiring the D&D license from TSR, this was prior to Wizards of the Coast, which was founded in 1990.
There is no general guidance in the rules
As far as I have seen, there are no official rules for claiming parcels of land. I doubt any rules like this will ever be written, or at least they will be very vague if they are. Historically speaking, claiming land was very dependent on which region you are in, and who you were operating on behalf of.
Some things to keep in mind is that the Forgotten Realms are a medieval-adjacent setting meaning that the rulers of a region typically have total say on land-ownership if they want to (and they often do for fortresses). I would strongly recommend trying to get the go-ahead from the ruler of the region before restoring a fortress to prevent the rule from simply staging their own claim, since theirs would be backed by their governing authority.
This is further reinforced by the appearance of land being granted as an alternative reward in the Dungeon Master's Guide:
Since a ruler is the entity mentioned that can grant you land as a reward, it is likely the same place to go to stake your claim.
In your specific case, Axeholm isn't definitively in any ruler's territory. The Sword Mountains are in a state of tribal conflict. However, getting the backing of either, or better yet both the Lords of Waterdeep, and Lord Protector Neverember of Neverwinter (the two closest major settlements) would help keep competing claims off of you, at least from the civilized world (such as Dwarvish heirs). Then you just need to protect the fortress against the orc tribes, and their ilk, in the region.
Example in existing adventures
There is a similar example in existing modules that illustrates how this process might look. In Rise of Tiamat, there is the following excerpt in Chapter 9:
As you can see, claims on strategic properties, likely including fortresses, is debatable. However, right of conquest is at least something that exists in Faerun. A suitable, but likely lengthy, argument to either of the powers I mentioned before could land you a deed to the fortress. That being said, once you've restored the fortress, other interested parties will likely make their own claims (whether legitimate or not). Holding such a property is as much a political exercise in the civilized world, as a militaristic one against the tribes.