Learn Farsi: من داشتم دیالوگ را زمزمه می‌کردم.

This is the exact structure you are learning for the Past Progressive! داشتم (dâshtam) acts as a helper verb to emphasize that you were right in the middle of doing something. It must be paired with a main verb in the past continuous, which here is the compound verb زمزمه می‌کردم (zemzeme mi-kardam). Notice that both verbs are conjugated for 'I'.

Can I put داشتم right next to زمزمه می‌کردم?

It is much more natural to keep them separated. The helper verb داشتم usually goes right after the subject, while the main verb stays at the very end of the sentence. This creates a frame around the object دیالوگ را (diyâlog râ).

Is را strictly necessary after دیالوگ?

Yes, because دیالوگ (diyâlog, a loanword meaning dialogue) is a specific, definite direct object here. You are talking about 'the' dialogue. Without the definite object marker را (râ), it would sound like a general activity of 'dialogue-whispering'.

What happens if I drop داشتم and just say من دیالوگ را زمزمه می‌کردم?

The sentence is still grammatically correct, but the meaning becomes broader. The past continuous alone can mean 'I was whispering the dialogue' or 'I used to whisper the dialogue'. Adding داشتم makes it exclusively the past progressive, focusing on that exact moment in the past.