Plusk: sort of, but perhaps not in the exact sense you mean, because you seem to have confused different processes.
The photographs most of us were taking until recently, when digital photography swept in, involved
# creating a (flexible) film negative in the camera (i.e.'taking the picture');
# 'developing' that negative to make it permanent, and then;
# making positive prints from it (by shining light through it on to photographic (light-sensitive) paper and in turn;
# 'fixing' those positive images to make them permanent.
[I used to do a bit of all this at one time, which was great fun.]
Making the positive print didn't adversely effect the negative original, so you could keep it, and make as many prints from it as you wanted. Negatives deteriorated slowly but so long as they were kept in good conditions (dry, not too hot, not too much light exposure, free from mould, etc) they lasted for decades.
Alternatively, slightly different 'transparency' film could be used in the camera. In this case the original film itself was transformed by the development process to produce a transparent positive, through which you could then shine or 'project' light to cast an image on to a surface. Home transparencies or 'slides' were usually made from frames measuring 24 x 35mm, the same size as most domestic negative films, but professional photographers often used larger film to produce transparencies of, say, 100 x 100mm because (for reasons I won't bore you with) this could produce better quality large pictures for magazines, etc.
[I've taken 35mm transparencies for semi-professional purposes - it's a damned sight harder as there's less leeway with the exposures and less opportunity for darkroom adjustment without a printing stage. I also used to use professionally provided transparencies of various sizes for illustrated postcard, magazine and book publishing.]
Positive transparencies would also keep for decades if not mistreated, and copies very nearly as good as the original could be made by flashing light through it on to another unexposed film using the appropriate equipment.
In either of these two categories, pictures could be 'faked' in various ways, either by treating the print or film directly with paint, chemicals, heat etc (the book cover artist Chris Yates used to create some spectacularly surreal artworks by these methods - see old Arrow SF paperbacks of the 70's), but most often by making multiple exposures either in camera or in the darkroom.
The Cottingley Fairy photographs, however, were made not on film, but as mentioned on glass plates. Such plates, often the same size as the intended final product, were coated with light-sensitive chemicals, carefully loaded inside light-proof casings into the camera, and then exposed to take the picture. They were than taken out (still encased), and developed in the darkroom.
[This I've never done, though I'd love to have a go.]
Depending on which of several processes was involved, this could result either in a glass negative from which good multiple prints could be made (just like the print-film process described above), or a positive image on the plate itself (unique, like the transparancy process, but not as readily projectable). To make copies of this positive image you would effectively have to re-photograph it, with (at that time, anyway) some loss of quality in the copies, which could be more positive plates or negatives plus prints. I'm not sure whether Arthur Wright used processes producing positive originals or more copyable negative ones (he could have used both with the same camera), but some references imply the latter. However, many of the published versions were copied from positive prints, not the originals.
There are a couple of reasons for using comparatively big, heavy, awkward, fragile glass plates instead of lighter film (which itself was invented pretty early on). One was that film can stretch and distort slightly, not usually a problem unless you want to take very precise measurements - which is why astronomers continued to expose (big) glass plates until quite recently for measuring exact star positions, etc. (I gather the last factory making them has just ceased production, but many thousands of plate exposures remain in astronomical archives.)
The other is that, while photographic film was quite difficult to make outside of specialist workshops, ordinary* plates could easily be created from plain glass and (noxious) chemicals by the photographer himself (* this didn't apply to modern astronomical plates, which used highly sophisticated, precisely appplied emulsions). Many amateurs used to do this as well as develop their exposed pictures. Elsie's father Arthur Wright certainly routinely developed his own exposures: it's unclear if he also made his own plates, but in any case the later series of photos were made on plates supplied by a third party (Edward Gardner) and developed by Arthur.
Phew! That's probably a lot more than you wanted to know, plusk. To finally address your questions:
# A competent darkroom operator could certainly copy original positive or negative plates as well as films and also make multiple exposures - note that despite her tender years Elsie, apart from being a good, trained artist, had actually been professionally employed as a darkroom operator to combine photos of dead WW1 soldiers with photos of their grieving families into composite images, prior to the appearance of the Fairy pictures. However, all of the Fairy plates were apparently developed by Arthur, not Elsie, ruling out post-exposure manipulation unless Arthur himself was complicit.
# Kodak didn't (at least at the time) authenticate the photos, saying there were too many ways to fake such things, though apparently un-named "expert photographers" reportedly declared the originals showed no physical signs of interference or multiple exposures, and Elsie with her professional expertise in these matters would have known perfectly well that such fakery would be easily detectable, but
# no plate manipulations would be necessary if the 'Fairies' were actual objects that had been in the original scene. There is of course strong if not 100% conclusive evidence that these objects were pictures of fairies, cut out of a particular children's book, touched up by Elsie, mounted on hatpins and deployed around the carefully posed human subjects in the scenes photographed.
