Those Philips Hue models with the abbreviation "BT" in the name support control via the Bluetooth app, i.e. no Hue Bridge is required. As far as I know, the "Basic" version of the "Iris" model is only available without Bluetooth (BT).
The Philips Hue Tap Dial Switch is generally compatible with Philips Hue products that are controlled via the Hue Bridge. Without a bridge, the Tap Dial Switch cannot communicate directly with the Iris BT lamp as it relies on the bridge to connect to other Hue devices. The Iris BT lamp itself is Bluetooth-enabled and can work with Amazon Alexa and Google Nest without a bridge, but a bridge is required for full functionality with the Tap Dial Switch.
Yes, but the colour setting that was set before switching off is no longer active when the luminaire is disconnected from the power supply. I have regulated it in such a way that I only switch the Hue lights on and off via the app, and not via a socket controlled by a switch.