I use the lamp in exactly the same way.
As long as it is switched on via the light switch on the wall, the lamp can be controlled via the app. It can also then be switched off and on - as long as the wall switch is not operated.
If the lamp is cut off from the power via the "normal", physical wall switch, the App or the Bridge can no longer control the lamp. Until the next time it is switched on via the wall switch.
According to my girlfriend, who can still hear perfectly well, unlike me, no. But it can't be ruled out that others in the series do something like that...
If everything is wired correctly, i.e. earthing is present, phases are not reversed, then the integrated dimmer is probably defective, but in any case the lamp.
No, a cable with a plug will not be included. Since very few people plug a ceiling lamp into a socket on the ceiling.
Max Hauri connection cable 3 m open-T12 (3m)
Max Hauri connection cable 5 m open-T12 (5m)
https://www.hornbach.ch/shop/Anschlusskabel-T12-TDLF-3x1-0mm-3m-weiss/5022603/artikel.html
Unfortunately, the specs are stored incorrectly. The bridge is not included in the scope of delivery. We have immediately forwarded the incorrect information for correction.