I am looking for a way to retrieve statistic counters for number of queries to Conf engine, number of failed requests, etc.
No such statistics is kept by ConfD, but you can do so yourself if you wish through for example audit messages notifications. See ConfD 6.4 UG Chapter 12.2. Audit Messages.
Then you can for example create a YANG model and store your stats in your format of choice in the CDB operational datastore. See ConfD 6.4 UG Chapter 6.8. Operational data in CDB