Assuming it is merely fibreglass or Rockwool, there is no reason to remove it. It doesn't deteriorate over time and is the same product with the same properties as the new stuff purchased today. As you say, it will add to the overall insulation performance of the layer.
Regarding insulation of the walls, it doesn't sound as if you have a conventional cavity (air gap between two leaves of the wall). So nothing to fill. There are also issues with installing foam next to timberframe. Suggest you ask a local company to take a look on what options there may be.