After a bit of macho wrangling, I read the manual and found out that the keyboard is designed for Mac for now (which doesn't make much sense as there are many more Windows users than Mac). If you hold ESC and ENTER for 3 seconds, it switches to PC mode and the keys work.

Yes, it works.

I have the function keys 1 -12 on my Bluetooth keyboard and don't need them on the number pad. I wouldn't know how to activate them either. Rather unlikely.

Yes, the product also works under Windows.

Unfortunately, I can't say yet, but when it was delivered, it didn't accept all the keystrokes before I reloaded it. Otherwise, everything has been fine so far. If you have the cable with you, it's no problem to connect it briefly to the PC when the battery is low.

Handling and construction look exactly the same. No idea if there are any technical differences.