Hmmm… some kind of Century face. But which one? I don’t
understand the serif on the “c”, it should be ball-shaped.

Yeah, it looks pretty much like Century Schoolbook, but the ‘c’ got me puzzled.

Here is a bit more from their website: — still convinced about century?

Now that’s Palatino.

The first sample you posted, however, is not Palatino.

Looking at the two samples again, I notice that they seem to have changed face mid-project? The two faces are wildly different, — leaves me baffled!?

Exactly. The first one looks like Century Schoolbook, whereas the second sample you posted is Palatino.