Is this sentence right?

Is this sentence right?
 

I stumbled upon this Spanish sentence together with an image:

"A ella le están dando la llave de su habitación."
She is getting her room key.

At the picture you see a receptionist giving a key to a woman.

I know the Spanish translation of course isn't a literate translation, but I suspect the Spanish translation itself for being incorrect, or at least it seems incorrect to me. I don't understand why the third person plural of estar (están) is used and not the singular form (está), and I also think "ella" and "le" should switch places.

This is what I would say:

"A le ella está dando la llave de su habitación."
To her (dat.) she (nom.) is giving the key of her room.

Or eventually, move the "a le"-part all the way to the end:

"Ella está dando la llave de su habitación a le."
She (nom.) is giving the key of her room to her (dat.).

Am I on the wrong track, or is the sentence actually wrong?

Thanks! :)

Oh, darn. I forgot the prepositional pronoun can have the form as "ella." It seems like I really was at the wrong track. But I still don't really understand how the prepositional pronouns work. Could someone help me out with this then? Are the prepositional pronouns simply the pronouns used after prepositions like "a," "de," "por," etc. (except "con")?

(By the way: This doesn't clear up the use of "están" in the sentence though!)

A ella le están dando la llave de su habitación.
A ella = to her
le = to a third person (ambiguous, so needs clarified - clarification accomplished with a ella)
están dando = they are giving
la llave de su habitación = her room key

They are giving her her room key. -or-
They are giving her room key to her.

Since there is only a single person giving the key away in the picture, and the present progressive tense is being used, I would opt for está dando. However, when talking about services rendered by an establishment in general, like at a hotel or a movie theater, the 3rd person plural is usually used. For example:
What movie is showing? ¿Qué película dan?

By the way, don't rule out a prepositional pronoun with con. Look at con ella. The preposition is followed by a prepositional pronoun. Contigo is simply a contraction of a preposition and a prepositional pronoun.

Ah, I get it now, thanks a lot, Rusty!

Could you verify what I said in my previous post?

Maybe some of the edits I did while you were responding serve to verify. I don't know what you're refering to.

The indirect object pronoun le, which preceded the verb in your sample sentence, is ambiguous (third person pronouns usually are). Therefore, a prepositional phrase that clarifies its meaning is usually included in the sentence elsewhere. In the sentence you cited, it began the sentence (preceding the pronoun it clarifies).
The prepositional phrase could very well have been placed at the end of the sentence:
Le está dando la llave ... a ella.
It is also possible to place it after the verb:
Le está dando a ella la llave ....

Just in case you were wondering, it is important to note that le is an indirect object and a ella is a prepositional phrase that happens to clarify the indirect object. The prepositional phrase cannot take the place of the indirect object. Its job is to clarify, or emphasize, the indirect object. Many English speakers look at this kind of sentence and think it's absolutely redundant to use both. We transliterate a ella le ... to to her to her .... There's no redundancy in the mind of a Spanish speaker. The phrase is perfectly clear and perfectly formed.