Solar-powered DC motor for mini fountain
The Bonus question is almost certainly the culprit. Under that condition, it is essentially the same as when the motor is stalled, or locked rotor condition.  When a motor is not spinning it does not generate any back EMF and so will act as a short.  The only current limit is in the DC resistance of the wire and/or the current limit of you source.
This condition creates a lot of heat, and can/will melt the insulation on the wire (even magnet wire insulation).  The other thing it can do is heat up the bearing or bushing for the rotor, which once that deforms also kills the motor.
A solution to the above, would be to use some sort of circuit as @Chris Stratton is describing in the comments of the OP.