Yes, a LR1 battery is included.

We are doing our utmost to be able to offer stock again. In the meantime, you can find alternatives from other manufacturers that may meet your needs via the following link: https://www.digitec.ch/fr/s1/producttype/detecteurs-de-mouvements-1602

Unfortunately, the supplier itself is still waiting for a subsequent delivery from the manufacturer. Currently, there is no information about the availability.

The manufacturer itself does not mention anything about water resistance of the product - so I unfortunately assume that the device is not waterproof.