How do you refer to key objects like the Death Star from Star Wars?

Late edit
The OP's clarification means this takes an entirely different turn. The answer below is what the movie makers call these.
A seller of 'imitation' objects would have to call them replicas, reproductions, models and miniatures. They could include the term icons, as in Flater's answer, or any terms that describes their purpose in-universe - but as they weren't in the movie itself, they cannot be considered props even if they were handleable, like a light sabre.
A replica really isn't a prop - to call it such would [perhaps falsely] convey a sense that it was from the actual movie.

I suppose it depends which version of it you're thinking of.
I can't think of one single word that covers it in all aspects.

Looking from the outside, in the early movies it's a miniature. These days, of course, it will be entirely CGI
From the inside, or when filmed outdoors at full size, it's a set, sometimes in a location.

A prop would generally be something small enough to pick up.
A light sabre is a prop, a spaceship isn't.
A character is generally 'something' that speaks or acts in some way.
Darth Vader, Yoda & Jar Jar Binks are characters, even though only one is directly played by a human.

I would tend to think that something as iconic as the Death Star or the Millenium Falcon would deserve a better name

If you're looking for a name for something that's iconic, it's (unsurprisingly) an icon, i.e. a well known symbol, emblem, or person that is idolized.

I agree with many of the already existing answers, but I would like to add a little more...

In Star Wars' case The Death Star(s) can be seen as a an iconic visual prop (model, set piece), a character (because it has a distinct look/feel that helps shape both Star Wars aesthetically and because big events happen to main characters there, making it more than just a setting), and a possible (by George Lucas' standards) MacGuffin, as it is also a plot device in the form of a mass super weapon that is directly tied to the plot of both A New Hope and Return of the Jedi.

In addition, because the Death Star doesn't just appear once, but twice, it also then becomes an over arching theme through much of Star Wars, but by expanding on the idea of important space stations (See High Republic's Starlight Beacon and Amaxine Station) or other kinds of similar super weapons (see: Starkiller Base). These are some of things that make Star Wars, Star Wars.

The Millennium Falcon is similar, but thematically tends to be in association with the identity of certain characters (Han, Lando, Chewbacca, L3-37, Rey, etc) who come to own or helm it: playing to broader theme of 'space pirates' and the like.

It serves as an extension to the identity of the characters who fly/man the ship, but also for most of the protagonists, it's a place where those characters often grow together. In the case of Rey, we also can view the Millennium Falcon as a baton being passed, making the ship apart of Star Wars ongoing theme of family and legacy.

It may be more debatable to consider it a MacGuffin however, as although the smuggling chamber, an ability to get places, a capacity to fight back might all be seen as things integral to the plot, it is more defensive against the bigger Macguffin or existential threat. It may be integral to the plot, but it is not necessarily driving the plot.

Now to your update: when you selling/buying merchandise for any well-known film or franchise then you are selling/buying: toys, games, books, comics, clothing, home decor, kitchenware, and/or other kinds of memorabilia (models, replicas, posters, autographed items, film stills/animation cells, etc)

I think your question is combining two different perspectives. The word "prop" is a behind-the-scenes word. In the Thor movies, there are multiple props for his hammer; perhaps one for close-ups and one that's easy to wield. But it's one entity in the Marvel universe.

"Character", on the other hand, is an analyzing-the-story word. Actors play characters in the same way that props represent objects in the story. But there is no special word for "object-in-the-story" analogous to the word "character."

There is a word for "place-in-the-story", that is, "setting", and the Death Star is sometimes definitely a setting. But other times, in analyzing-the-story contexts, it's just whatever it is the characters think of it as. Or, more abstractly, it's a key plot element. It is true that sometimes especially important inanimate objects are metaphorically described as characters, but I don't think the Death Star is a good candidate for that.

Behind the scenes, the Death Star has been represented by models, which I think count as props, but also by sets when the characters are inside it. It's also been represented by matte paintings and computer models. So it's not any one of those things.

Out-of-universe, and from a commercial point of view, which seems to be what you're after, these objects can be described as props, memorabilia, collectibles, or models (as you yourself describe them :):

• The word prop usually refers to the real object used during filming. It is unique or has a very limited edition.

• 'Memorabilia' - in this context - is used for anything from unique items to autographed objects to posters.

• Collectibles usually are on the mass-production side of the spectrum, intended to be collected by fans.

• Since a model is often a (scaled) version of the thing it represents, that would be a good word for describing the objects you list to be used for "a site that sells models of game and movie heroes", as can be demonstrated by googling object + "model":

  • Death Star model
  • Millennium Falcon model
  • Rick's portal gun model
  • T70 X-Wing model
  • and e.g. Batman model (or 'action figure')

  As you can see, it can be used for weapons, spaceships, handheld devices, and characters.

Diegetically, in the Star Wars universe, the Death Star is a superweapon as well as a space station.
It is no character, in the sense that it has no free will nor personality, in the narrower sense of the word (to quickly name somethings I think can be considered prerequisites for what constitutes a character). Neither is it played by someone.

Props can also occur in-universe, for example as a dud, a replica, or 'switcheroo'.

A different angle suggests that "it depends."

It may be "a prop" if it's one of several more-or-less identical items that are more-or-less interchangeable. In-universe examples might be light sabers, X-wing fighters --- even clone soldiers or slaves. It's not about who they are, but what they are.

It may be "a character" if an item is referred to by name rather than type. Moreso if non-identical items are used in several films as if they were the same (named) thing, because it then becomes more about the identity than the actual object.

Given that the Millennium Falcon is one specific craft of the YT-1300 Corellian light freighter class, consider:

Is "The Death Star" a named entity, or is the "death star" just one instance of a DS-1 Death Star Mobile Battle Station? Wookieepedia does not make this entirely clear, and I for one am not sufficiently well-versed to make that call.

The difference has interesting consequences. Case in point: pretty much anyone can style a DeLorean as that particular car because, in-universe, it's always referred to as a "time machine" --- whereas if anyone were to make even a crummy pony car and referred to it not as a "car" but as "Eleanor" then, regardless of whether or not it had any similarity to an actual Ford Shelby GT500, they'd find their car confiscated in a hurry because "any car of that name" is a trademarked character, precisely because different actual cars were used for that role.

Although the question has been answered, I'd like to suggest one possibility that doesn't seem to have been mentioned. From similar series, for iconic vehicles like the Millennium Falcon or Death Star the term "hero/villain vehicle/ship(etc)" has been used a lot.

They aren't characters in their own right, but they have taken on personality in a way, and are also instantly relatable to the good or bad guys - especially useful for marketing.

One - derogatory - term for it would be MacGuffin.

According to Wikipedia

In fiction, a MacGuffin (sometimes McGuffin) is an object, device, or event that is necessary to the plot and the motivation of the characters, but insignificant, unimportant, or irrelevant in itself.

The irrelevance of the death star is of course up for debate here.

Also from Wikipedia:

In contrast to Hitchcock's view of a MacGuffin as an object around which the plot revolves but about which the audience does not care, George Lucas believes that "the audience should care about it almost as much as the dueling heroes and villains on-screen." Lucas describes R2-D2 as the MacGuffin of the original Star Wars film, and said that the titular MacGuffin in Raiders of the Lost Ark was an excellent example as opposed to the more obscure MacGuffins of the next two Indiana Jones films.

Very much in line with that logic the death star is an object, that is basically one of the main "villains" of the movie and entices a lot of audience emotions. But if you look at the device itself, it does not really have much relevance apart from being the "destination" of the journey. (unless you happen to live on Alderaan of course)