No, the DJI Osmo Pocket 3 is not waterproof. It should not be used in rain or underwater without a dedicated third-party waterproof housing.
The battery lasts up to 166 minutes when recording at 1080p/24fps. It also supports fast charging, reaching 80% in approximately 16 minutes.
Yes, it has a built-in Wi-Fi and Bluetooth module for direct connection to the DJI Mic 2 transmitter, or you can use a USB-C to 3.5mm adapter.