Does anyone know what happens to existing cloud functions while a new version is being deployed? Is there going to be some (even if it is small) outage of service for our app while we deploy a new version of cloud functions?
This is particularly important for Firestore triggers where certain logic depends on a trigger to be run in response to some action in Firestore documents. An outage of cloud functions could leave the database in an unexpected state if some triggers where not run for a period of time.
Calls will keep being routes to the existing functions until the new version is deployed. At that point, new calls will be routed to the latest deployed version.
Since you seem concerned with data consistency, keep in mind that:
Background functions are invoked at least once. ... The system might, in rare circumstances, invoke a background function more than once in order to ensure delivery of the event.
From the Cloud Functions documentation on execution guarantees.