Hello,
Thank you for uploading the weather file.
To answer your questions about Case1 and Case2: For the peak shaving options, SAM is trying to dispatch the battery to minimize the demand charge for each month. At the beginning of each month, it does not discharge the battery until it reaches full charge to ensure that the battery is fully charged at least once a month. That's why for some months, you will see that the battery state of charge gradually increases until it reaches the full charge capacity (an input on the Battery Storage page that you can change -- it is 95% by default for Lithium-ion batteries). It uses power from the PV array to charge the battery, so it can take a few days to fully charge the battery, depending on the size of the array.
For Case3, I will need to investigate and get back to you.
As for a metric for your optimization, SAM does not generate one that indicates the amount of fluctuation. You could write an LK script to develop your own metric. For an introduction to LK scripting, please see this webinar recording:
sam.nrel.gov/node/69358
Best regards,
Paul.