Question about DJI Osmo X3 4K UHD Gimbal & Camera Kit + Microphone

No, I've never had that - my Osmos hang up from time to time = they won't start again except with a reboot.
Try the following - DJI released a new firmware the day before yesterday - copy the firmware file to the root directory of your micro SD card.
Reboot the Osmo (hold down the record and trigger buttons at the same time and then the power switch down) - the upgrade should take about 20 minutes, the LED will turn static green again once the update is complete.

Yes, as long as you have updated the Inspire with firmware 1.5.0.30 or newer. Important - The Osmo X3 Cam must be on the drone during the Inspire firmware update in order to be recognised.
I am very happy with it so far, I recently used 2 Osmos remotely on a tripod to record a concert for a Swiss band:
https://www.youtube.com/watch