Mole that has split skin now have hole or crater. What to do? (photos)

You should go and have this evaluated by a doctor. Instead of a simple mole, this may have been skin cancer. Basal cell cancers start as bumps on the skin, but as they develop they can ulcerate and look like this. Hopefully it's not that, but you need to have it checked. Good luck.

This appears to be a basal cell carcinoma rather than a mole. In fact, with an opening as demonstrated in the picture, this is consistent with a so-called rodent ulcer...a particular aggressive form of a basal cell carcinoma. I would strongly urge you to consult with a dermatologist or plastic surgeon to have this taken care of.