This answer may be way overdue, but I would like to add my thoughts.
But beings such as the Bäckahäst would cause some trouble here. The
common translation into English here is Kelpie, but to me, Bäckahäst
and Kelpie are two different beings, one from Norse folklore and one
from Scottish. So to translate Bäckahäst into Kelpie would be adding
I agree with the above. Don't translate then. This kind of stuff really boils down to what you really emphasize. If you want to find the closest equivalent in the target language's culture, then you may use Kelpie. Here, you are helping English speakers bring up imagery about what they already identify with and know something about. If you want to emphasize on the cultural nuances of Bäckahäst, then you may use Bäckahäst.
But keeping "Bäckahäst" as the name also causes some questions for me. Namely, how to add grammar stuff to it. The Swedish way to put Bäckahäst into plural would be to add "-ar" at the end of the word (Bäckahästar), but the English way is to add "-s".
Using the English version seems to me like the logical way, but it makes the inner me—reading the word the Swedish way—cringe.
People who speak Chinese as a second language and English as a native language may add -s to 汉语 in an otherwise English document. cringe Somehow, in their minds, they perceive 汉语 as singular. By itself, 汉语 is neither singular nor plural. Given that Bäckahäst is a foreign word, you may choose to italicize it to emphasize on the foreignness or keep it as Bäckahäst out of personal preference. As a foreign word, Bäckahäst should not follow English rules. Now, if you make up an English word based on the original word, like Backahast, by removing all the diacritical marks, then you may treat this as a native English word and thus add -s. So, the plural of the English word would be Backahasts. The original Swedish word would still be Bäckahästar. There, problem solved.
This question reminds me of my own question: How to describe a mythological creature that English has no vocabulary for? But the focus is on Chinese folkloric creatures. 妖, 魔, 鬼, 怪 have been translated into many things, all depending on context. Translators may choose words like demon, ghost, ghoul, spirit, and monster. 兽 (Pinyin: shòu ; Jyutping: sau3) is likewise difficult to translate. A notable Chinese dictionary Xin Hua Zi Dian (新华字典) may describe this as "有四条腿，全体生毛的哺乳动物" or in English translation "four-legged mammal". A mammal by definition has fur and consumes mother's milk. Okay, then what's 怪兽? Pleco translates this as (1) rare animal, (2) mythical animal, and (3) monster. The real meaning of 怪兽 lies in Chinese literature, including foreign literature in Chinese translation. It is possible to transliterate 妖精 into yāo jing (based on Pinyin), but nope, translators seem to be mostly interested in using existing English vocabulary. When 妖精 is translated as "demon", English speakers would think hell and bad stuff especially in the context of Christianity.
All in all, I think this just depends on what you want to emphasize and what you want to connote.