There is one gray cloud in the sky. Should be an acceptable translation for "ενα γκρι σύννεφο υπάρχει στον ουρανό."
Why is υπαρχει not at the start of the sentence here? Would it also be accurate to translate this as "A grey cloud is there in the sky'?
It would be... except that word order doesn't work in English. Well, maybe it's technically allowed (I'm not a linguist) but it definitely sounds VERY wrong to my native English ear.
Greek is very flexible with its word order, so Υπάρχει could also go at the start of the sentence.
You're right and your native ear didn't let you down. The usage of "there is" maintains a certain word order in English so this sentence needs "There is a gray ...".
Is "a gray cloud exists in the sky" unacceptable? Does that sound weird?
Sorry to say but I agree with your idea. We just don't say "a cloud exists..." You'll see from the Drop down hints that we give the whole translation, and not just the word, right at the top. That is to assist you in learning the correct translation. The other words are there for reference for other contexts just as you might find several definitions in a dictionary.
Yes, they are different cases (declensions) of the same word, therefore each one is used in a different place in a sentence. https://en.wiktionary.org/wiki/%CE%BF%CF%85%CF%81%CE%B1%CE%BD%CF%8C%CF%82#Declension
Check the Tips and notes sections under the lessons (available only on the desktop website - not the apps) for grammar information.