Learn Italian: Dopo il lavoro ci si addormentava velocemente. - After work, one used to fall asleep quickly.

The verb for "to fall asleep" is reflexive: addormentarsi. Normally, the impersonal form uses si (like "one eats" = si mangia). But if we used si with a reflexive verb, we would end up with si si addormenta. To avoid that awkward double si, Italian changes the first one to ci, creating ci si.

Is addormentava conjugated in the singular or plural?

It is in the third-person singular (he/she/it form). When using the impersonal ci si (meaning "one" or "people in general"), the verb is always conjugated in the third-person singular, just like with the regular impersonal si.

Why is the verb addormentava in the imperfect tense rather than the passato prossimo?

The imperfect tense is used here to describe a recurring habit in the past. The English translation "used to fall asleep" gives this away. If it were a single, specific, completed event, you would use the passato prossimo: ci si è addormentati.

Could I use the verb dormire instead of addormentarsi?