Is it yours?
It is yours?
Can #2 ever be appropriate? Does it exist to facilitate placing emphasis on the personal pronoun?
The first form, with inversion, is the 'canonical' form for questions.
The second form, with no inversion, is typical of "echoic" questions, which repeat the substance of a previous speaker's assertion with interrogative intonation, and usually with one term emphasized and possibly replaced with an interrogative, in order to request confirmation that the questioner has indeed understood the assertion correctly.
A: That's mine.
B: It's yours? I think not; it looks like mine to me.
Yes. Whilst the interrogative is a straightforward question, the indicative followed by a question mark merely seeks confirmation of something about which the speaker has been very surprised to learn.
They are friends? The house is being sold?
It is a perfectly usual form. When spoken the emphasis goes heavily upon that part of the information which has come as a surprise.
For example - in the case of The house is being sold? the emphasis could go on either house or sold depending on which item had come as a surprise.
Let's say I know that someone is in severe financial difficulty, and has started selling some of his or her assets. I have just been informed that they are selling their own house. I might then inquire The house is being sold?
However let's say I am particularly attracted by a certain house which I would like to own. Someone informs me it is being sold. Then I might seek confirmation that I have heard them properly by saying The house is being sold?
"It is yours?" and "It's yours?" are used in a number of ways (often depending on how they are said as well) that are not appropriate for "Is it yours?" to be used.
Does it exist to facilitate placing emphasis on the personal pronoun?
"It is yours?" often functions to put the emphasis on "is", whereby the person asking the question can seek some assurance or confirmation of rightful ownership, without accusing the other party of being a thief (or potentially a thief).
So someone returning to a store / theatre / restaurant could say: "I left my jacket here last night; that's it hanging over there." Asking "It is yours?" can be done politely enough, but using "Is it yours?" is harder to do without sounding accusatory, however there is great flexibility in there, depending on how it is asked.