More or less. In my layman's understanding: Black holes 'evaporate' slowly through Hawking radiation, losing mass as a function of their surface area (simplistically, particle/anti-particle pairs 'pop out of nothing' near the event horizon, one gets swallowed up the other escapes, this means a net loss of energy, which has to 'paid' by the black hole losing mass, think E=mc²).

Since a black hole behaves (geometrically) like any other sphere, the proportion of its area to its volume will grow as the black hole loses mass (i.e. it will have more and more relative area the smaller it gets), this process speeds up over time thus ending in what I guess you could call an explosion (more a whimper than a bang, to borrow a phrase).

Part 2 of your question: We don't know.