If the heater core is leaking you'd be losing engine coolant but it would drain onto the ground. The combination of symptoms suggests that drain is blocked and condensation in the drip pan is the cause of both of them. Look under the hood on the passenger side of the firewall for a 4" rubber hose with a right angle bend hanging down. Squeeze that hose to try to dislodge the blockage. If nothing comes out, squeeze the wire ring that holds it on, remove the hose, then carefully stick a pencil into the spout to clear it.