Is written a noun

No, the Word 'written' is the past participle, past tense of the verb to write (writes, writing, written). The past participle of the verb is also an adjective, a Word that describes a noun. Examples:

Verb: We have written a list of everything we need.

Adjective: A court reporter is responsible for a written transcript of a trial.

The noun forms for the verb to write are writer and the gerund, writing.