Does the cable plug go fully into the socket or is there a noticeable gap between the phone and the plug?
If there is a noticeable gap the charging socket needs to be cleaned with fine tweezers, or if needed a toothpick / sim pin eject tool. Be careful of the pins at the bottom of the charging port as they can be damaged if pushed against when cleaning the port.
For the headphone jack problem. The port either needs to be replaced or the housing replaced (if it is bent right at the headphone jack. It could also be the same problem of dust build up in the headphone jack port.