Yes, these are compatible. The difference to the CR2032 is that the ML2032 is rechargeable. The last two digits (here the 32) stand for the "thickness" of the battery. This is identical here, i.e. the same "thickness".

Yes, but keep in mind that the ML2032 is rechargeable.

In terms of form, yes. However, if the device is not explicitly designed for battery operation (or both battery and rechargeable battery), the device can be damaged.

Yes, but rechargeable - e.g. in a solar-powered Logitech keyboard.

No