Why eines is used here instead of eine or ein?
Eine is correct. Einen would also be correct. (depending on context and the gender of the object)
Ein is incorrect because it is nominative and not accusative.
For example: "Ich habe einen Apfel. Hast du einen?"
So I can say "Ich habe eine Erdbeere. Hast du eine?", right? Is "eines" a neutral article, which you can use instead of "eine" and "einen" in such contexts? Can I also say "Ich habe eine Erdbeere. Hast du eines?" ?
Good question. No, you would have to say "Hast du eine?" to match the gender to Erdbeere. (I wasn't sure myself so I checked with a native speaker)
You could go with "Ich habe win Mädchen, hast du eines ?" to match the neuter. It all depends on context and on what you are referring to !
'Have you one thing' is really horrific English. Is there a better translation?
My best, prettiest translation would be "Do you have one of those?", depending on context.
So 'Do you have one thing ? ' is not a correct answer.
It could be a thing or a person or an animal.
there is another phase that duolingo has 'haben Sie eines?' that is the same translation, which one is correct and which is incorrect?
They're both correct. "Hast du" is for informal situations while "Haben Sie" is for a more formal you.