I want to write in Spanish "Is this girl happy?". What I came up with is "Está esta niña feliz?". It looks strange and sounds unclear, but I don't want to use "Es esta niña feliz?", because this is a temporary state. Is it a right translation? Is "está esta" ever correct in a sentence?
Your sentence might sound a little weird to your ear because this particular combination of verb and adjective isn't customary. Most often you'll find these two arrangements:
In addition, "esta" isn't used as often as "this" is used in English. When it's clear from the context which girl we're talking about, we'll generally just use the definite article:
¿Está la niña contenta?
And if possible (in other words, when the context is clear enough), we'll omit "la niña" completely:
Now, I'll tell you where one will see the demonstrative pronoun esta used on a regular basis -- when you're distinguishing between this and the other. (Note, "esa" [that] is generally avoided, see What does "ese" mean?, but that's okay, "the other" [la otra] works just fine when making comparisons.)
For example, suppose we are analyzing differences between two girls based on their demeanor in a videotape of a classroom lesson and activity. We might point out:
Esta niña está contenta, pero la otra no.
If A is wondering how B perceives the two girls, A might ask B:
¿Está esta niña contenta?
Or, more commonly:
¿Esta niña está contenta?
In this same scenario, perhaps B already pointed out
La niña al fondo no se ve muy contenta. [The girl at the back doesn't look very happy.]
And now, to point out the contrast, B might ask A's opinion:
¿Qué crees, está esta niña más contenta [que la del fondo]?
I had to work a bit to come up with a conceivable context for the question -- but it certainly is possible.