.show ingestion failures
outputs errors in the ingestion process. I however did not find a way to get list of successfully ingested items, as well as inspect the ingestion queue (names of the items) and current status (what is being ingested at the moment). Is it possible and how to view that information?
ADX is optimized for high throughput, therefore it is not optimized for exposing individual ingest operation tracking by default (that level of granularity puts extra load on the service). We also do not expose detailed information on the queues, definitely not listing the ingress queue items.
You can track all the ingest operations (failed/succeeded/both) by setting up Diagnostic Logs with Azure Monitor.
An aggregated view on your cluster via metrics is also available. Please see Monitor Azure Data Explorer performance, health & usage with metrics and Monitor batching ingestion in Azure Data Explorer.