Hello,
Issue1# - Sounds like you have a bad output jack or a short somewhere. Output jacks do wear out after a long time of hard use. Another thing to check for is maybe a wire was frayed on the I/O wires or one of the lugs on the output jack are touching the ground paint inside the cavity when a jack is plugged in, and running the cable through the strap cable acts as a "tensioner" for the cable, causing the jack to pull away from whatever it's shorting out on. Might help to bend some solder lugs and/or reposition the jack. It could also just be a solder joint that has gone bad as well.
Sometimes I also find the individual strands of wire inside the wire used to wire guitars can get "stray" and cause shorts. Not sure why this happens, but sometimes it does. Helps to have a magnifying glass to find these issues.
#2 - Definitely sounds like a bad switch, a common problem with Jag-Stang and Mustangs, especially with the original switches used in them. Those too can wear out. The faint sound sounds like either one of the sliding contacts inside the switch is no longer "jumpering" the 2 contacts it touches (or frozen in one spot), or you have a short that has developed on a part of the switch assembly either from a failing switch or maybe a lug came loose (they sometimes do) and is touching the shielding paint.
