Answer to first question: you can use Reporting Task's to get processor status and enrich/trim the information as per you need with in NiFi
or you can configure downstream queue for relationship Original from InvokeHTTP procesor and have count on that ,something similar on the lines https://community.cloudera.com/t5/Support-Questions/NiFi-Count-Fileflows-via-attribute/m-p/178860
Answer to Second question : NiFi stores processor related logs under nifi-app.log file which is by default located under /var/log/nifi/ , By default NiFi Processors only prints logs for start and stop operations and Warning and Error associated to the processors , user wont be seeing any events on what is being processed by processor until DEBUG is enabled for Processor class, which is only recommended to use in case of detailed information needed while troubleshooting any problem for short term period. You can filter specific component logs in nifi-app.log by using their component ID.
Thank You.