FANMISCreative Mens Binary Matrix Blue LED Digital Watch Fashion Classic Black Plated Waterproof LED Backlight Bracelet Watches

Q: Is this waterproof? If so, how deep?

The advertisement shows it under running water, in a glass of water and also covered in soap suds. It better be waterproof or I’ll be returning a drowned watch. Just sayin’.

Q: will the black painted surface rub off over time?

It's possible. But it's ion plated supposedly, so hopefully the finish will last a while. As for the numbers, they might be more susceptible to being rubbed off. I've had this watch since February 2017 and it shows no sign of the finish or numbers coming off so far.