It's not much different than the Prius in overall operation. The 12v battery powers all ancillary systems like any other vehicle such as lights, radio, etc.. While the vehicle is running/in 'Ready to Drive' mode there is a DC-DC converter that is active and takes power from the traction/high voltage battery and converts down to the 12+V to power those systems and keep the 12v battery topped off. Same operation as an alternator on a non-hybrid/EV, just fully solid state and not reliant on the ICE. It operates in EV modes as well.
There is no direct way to actually charge the traction battery to a significant degree while driving. There is a 'button dance' with the EV mode button that can be done to inch the charge level up but charging from the ICE alone is inefficient. For a number of reasons, it is usually recommended when driving over 50mph or on the highway/freeway to switch to EV Later mode. This will save the current plug-in charge for use later and drop back to hybrid operation. There's also no official way to upgrade the battery capacity. A few owners have hinted at trying to hack something together, but nothing has come of it. The vast majority of owners don't care to attempt it and are happy with the range they get.
The C-Max does get noticeably less fuel efficiency than the Prius. Most consider it a worthwhile tradeoff for being a little more comfortable and having a bit more pep than a Prius would.
As far as range goes, being a 2013 it could have a degraded battery depending on how the previous owner(s) took care of it. Unfortunately due to poor programming on Ford's part, it is very easy to inadvertently degrade the battery if you 'just drive' and don't take proactive measures to prolong the battery life. Your miles of EV range could also be skewed if you JUST bought the vehicle as it will be based off recent driving, HVAC usage, ambient temp, etc.. There's a reason it is often called a 'guess-o-meter'. There is a much better and accurate way to get an idea of what battery capacity and wear you're dealing with:
Fully charge the vehicle.
Drive in EV mode only until the plug-in charge is depleted. Ensure the ICE does NOT run or it will skew the results. So you may want to stay off highways/freeways during this test, limit use of cabin heat (though in the current summer season, this may not be applicable), etc..
Once the plug-in charge is depleted, find a place to stop safely as soon as you can and shut off the car.
You should then have a trip summary show on the dash including the kwh used. This should give a relatively accurate gauge of battery capacity. 5.5kwh is around what a brand new battery off the factory floor should have seen. 4kwh+ is still good. In the 3-ish range or below is where degradation starts to get bad.