Learn Russian: Рукопись редактируется редактором. - The manuscript is being edited by the editor.

In Russian passive sentences, the person or thing performing the action (the agent) is put into the instrumental case without a preposition. Since the sentence means the editing is done by the editor, редактор becomes редактором.

Why does the verb редактируется end in -ся if the manuscript isn't editing itself?

Adding the reflexive ending -ся is the standard way to form the passive voice for imperfective verbs. It changes the active meaning (edits) to a passive one (is being edited).

Is рукопись the subject of this sentence?

Yes! In a passive sentence, the object receiving the action becomes the grammatical subject and takes the nominative case. Рукопись is a feminine noun ending in a soft sign, so its nominative form is just рукопись.

Is it normal to repeat the same root back-to-back like in редактируется редактором?

Yes, this happens often in Russian! Because Russian builds families of words from a single root, you will frequently see a verb and a noun with the same base right next to each other. Here, both words share the root for editing.