Does damage to the host-object cause Disturbance if the Kyriotate of Jean deliberately damages it? Dissonance?

Yes to the disturbance, no to the dissonance. When you harm a vessel, it sets up unpleasant discords between the Kyriotate's soul, the vessel, and the owner's soul. This wouldn't occur with non-living vessels.

However, the GM is quite free to rule that destruction of the item (via the Kyriotate's connivance or not) causes the Kyriotate Mind hits or other such mental trauma. It's suggested that it prevent the Kyriotate from possessing anything else for a short time, at the least. (See a nother FAQ, further down.

More.

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