I am going to make an effort to decode Swiftalu's hints here.
1. Their pup's name is Marshmallow.
Because Swiftalu listed it as a hint on their profile, I'm guessing the name marshmallow has some correlation to the traits of their pup. I think the most obvious qualities of marshmallows are their fluffy texture. Using this as a basis, I would narrow it down to these pups:

This one is the most obvious fluffy candidate.

Not quite as obvious, but this one has the clouds on it that seem very light and fluffy. (though I am suspicious because Swiftalu seems to have posted about this one and included it in the dressup hint and that makes me think it might be a red herring)

This is the least obvious of them in terms of fluff but Marshmallows got fluff but look smooth and the neck of this one feels very reminiscent of some marshmallow candies. Plus, let's be honest, it just feels fitting as a name.
2. R2C11
This was solved as a hint to be the 'I believe in dragons' stamp in Swiftalu's signature. This makes it feel like an obvious allusion to the dragon style pup but I will say that the cloud pup does have that sky theme that could point to a possible dragon inspired final growth.
I do think, however, this rules out the Fluff pup.
3.
https://www.chickensmoothie.com/viewpet.php?id=275406289 The first Dressup
Now this was a little tricky for me because I wasn't sure if it was one aspect of the dressup, a few aspects, or all of them. So naturally I just analyzed all of it.
The two obvious aspects are the plushie and the sun/clouds. The first points me towards the dragon pup again because the scales and reptilian look (I don't know if the plush is a dragon plush or not) and the latter points to the cloud pup because of the sky view (plus the pup dressed up is the cloud pup). However, the sky theme could also fit the dragon pup.
Fitting in the other parts of the dress up was a bit more difficult but the horns make me think of the dragon pup because some dragons have horns and the dragon pup has spots on its head that could potentially become horns.
The dress up also has a lot of outwear on. This works with the dragon pup as well because of the neck edit, which looks a little like a cowl scarf (also a piece of outerwear).
4. The Dress Up that hasn't been found
I'm guessing that this is one of Swiftalu's hat friend dress ups. I haven't entirely decoded this but both of the dress ups I'm referencing show a previous staff litter newborn with a hat on. Thinking of this mixed with the previous dress up hint, I think it's pointing to either headgear in general or cold weather wear, both of which could be exhibited in the adult form of the dragon pup.
With all these hints in mind, I'm thinking that this dragon pup:

Is Swiftalu's.
Feel free to let me know your thoughts, whether you think I missed something, or got something completely wrong.