Pixhawk 2.4.8 altitude oscillation, and other issues

I don’t think so. Even with a 6S Lipo it’s underpowered at that weight and you have a Li-Ion that’s dying trying to provide power.
Got any 15.5" props? That would get you closer to a flyable thrust/weight. Won’t fit the frame I guess…

When then either my scale is wrong, the thrust specs are wrong or something else is going on.

Drop the take-off weight to 3.2kg and put a 6S battery on there that can supply sufficient power and it will be where Arducopter needs to be for proper stability.
NEVER, should there be a thrust loss error.