It is a type of Opuntia, although I am not familiar with the exact kind.
If you bought it from a store or nursery I would repot it with fresh, well draining soil. I also wouldn't offer any to a tort for about a year due to pesticides and chemical fertilizers that have been used on it.
Good point!The thorns can be burned off or scraped off. My mom, back in the day would blanche the thorns off the fruit of hers in boiling water.
It is alot easier to use the thornless varieties though.