Learn German: Zum Glück verarbeiten wir ihn miteinander. - Fortunately, we process it with each other.

In the German Mittelfeld (the space after the conjugated verb), a pronoun subject like wir strictly precedes a pronoun object like ihn. Because both are pronouns, the subject takes priority and stays right next to the verb.

How would the word order change if the subject was a noun, like die Kollegen (the colleagues)?

If the subject is a noun, a pronoun object like ihn will usually jump ahead of it! You would say: Zum Glück verarbeiten ihn die Kollegen miteinander. Pronouns prefer to be as close to the conjugated verb as possible, so an object pronoun will cut in front of a nominal (noun) subject.

Why doesn't the ver- in verarbeiten go to the end of the sentence like a separable prefix?

The prefix ver- is inseparable and stays permanently glued to the verb. A good rule of thumb is that prefixes starting with an unstressed syllable (like be-, ge-, er-, ver-, ent-, and zer-) never separate.

Does verarbeiten refer to processing physical materials or emotional events?