Because adjectives in Italian usually agree with the noun in gender and number.
Since pagina is feminine singular, the adjective must also be feminine singular:
So:
Yes. That means The page is empty.
The difference is:
So questa specifically points to this page, while la simply means the page.
Not exactly.
They are close in meaning, but the focus is different.
In Questa pagina è vuota, you are talking about the page and saying what condition it is in.
In Questa è una pagina vuota, you are identifying something as an empty page.
Then both the demonstrative and the adjective change to match the plural noun.
For feminine plural:
Compare:
You can see all the agreement changes:
Yes. Like empty in English, vuoto/vuota can be used literally or figuratively.
Literal:
Figurative:
So in this sentence it most naturally means the page has nothing on it, but the adjective itself is broader than that.
Yes, completely natural.
It is simple, correct, and idiomatic Italian. A native speaker would easily say or understand it in contexts like:
It is a very standard example of Italian agreement: