It sounds like the cover lets UV through -- at least some. That would explain the variation on sunny vs. cloudy days. See if you can check the loss overnight. So add chlorine at night with the pump running, wait at least 30 minutes or up to an hour, then check FC levels (you can then turn off the pump if you don't normally run it at night). In the morning, turn on the pump if it hasn't already started, wait at least 15 minutes, then check the FC level (early in the morning before the sun gets too high in the sky. What is the FC drop? That will tell you if you've got something consuming chlorine other than sunlight.

The loss is normal if the cover lets UV through so let's assume that's the case. The overnight (non-sun) loss is really the key so let's see what that is before jumping to conclusions.

The pH drop is still a mystery. Though you have little splash-out, check the pH of the fill water just in case (maybe there's a leak in the pool -- doubtful though).

Richard