Is there a way to view the call information that can be found on the phone such as received calls, placed calls, and missed calls?
Sorry I'm not 100% sure whether you are looking to view this information on the phone (which you can generally do by visiting the 'Directories' section on a lot of Ciscos), or view this information from the CUCM server (I suspect this is the case).
You want to look into Call Data Records (CDRs), which are records captured for each call made through the system. Note that this may not neccessarily be happening by default and may need some configuration. On version 7.1 of CUCM at least, you can find it under Tools in the Cisco Unified Serviceability section of your CUCM web interface.
There is quite a bit to getting a full understanding of it (which I certainly dont have) but this should hopefully lead you in the right direction.