Can I use face products under the mask?
Yes you can, but you need to be sure that the products that you are using are safe for the lower temperatures before use.
Can we use it overnight during sleep?
You could try, but it won't stay cold all night, at the most it will be chilled for around 1 hour. You might it nice to fall asleep, but it would be uncomfortable to sleep with.
Can you heat it in a microwave?
No, you cannot.