Ihr Antrag ist abgelehnt: what does it mean and what structure is used?

Answer 1

"Your application is denied."

This is a passive construct in which the verb "ablehnen" (to deny) is turned into the adjective "abgelehnt" (denied). The active sentence would be: "Wir lehnen Ihren Antrag ab." (We deny your application.) Note that "ablehnen" is a separable verb, which splits up and sends the prefix "ab" to the end of the sentence.

HTH