Yes

Yes, it's in.

Mine had everything included in terms of electricity: you can see this in the last picture (packaging on the bottom right) where it says "Low Voltage included". It is a small power supply unit (transformer) with a piece of 24 volt cable (IP67 outdoor) on one side and a 220 volt cable with plug on the other. For the 24 volt connection of several outdoor lightstrips or luminaires, one can consider the purchase of a larger Philips Hue Outdoor power supply of 40 watts or 100 watts. For control (light intensity/ colours) via WiFi, e.g. from a mobile phone, a Philips Hue Bridge (or a similar ZigBee device) is required.