To fix the JST.

Use a PIN to release the terminal connector which is in the plastic.

Normally this connector is crimped around the wire.

If the wire has pulled off, you may be able to open the crimped area with a sharp knife ( CAREFULLY! ) and then use pliers or a crimping tool to get the wire back into position.

I always give these a touch of solder as well to prevent re-occurance, but you have to be extremely careful not to change the basic shape of the terminal due to excess solder, etc.