No way to determine EV vs HV miles.
- Is there a function to check battery health, charge cycles etc?
- Is there a way to see how much of the milage was driven in EV mode vs. HYBRID?
There is a measurement for battery capacity stored in the Clarity computer which will give you an idea how much the HV battery has degraded. Any Honda dealer can get this number for you, although they would likely charge you for it unless you are already paying them to inspect the car. Any independent shop that has Honda's i-HDS diagnostic software can check it also.
You can also check it yourself with an inexpensive OBD-II reader and a free Bluetooth app. You need a specific OBD-II reader which is the Vgate iCar Pro and also download the Car Scanner app to your phone (Android or iPhone). You can get familiar with the reader and the app by trying it out on your Odyssey (other info not battery capacity), then change the vehicle type in the Car Scanner app to Clarity prior to going to check one out.
There is a thread with more details about it at this link:
(UPDATE - This thread was started when the only known way to check battery capacity was through the dealer. The general information below about battery capacity is still valid, however starting in post #6 there is information about checking battery capacity yourself using an inexpensive and...