Internal Wall Insulation on Carpet/Wood Floor

Apologies but from my understanding to the following question: you want to insulate the wall internally without removing the carpet or wood floorings! SURE YOU CAN. PROTECT THE FLOOR USING DUST SHEET OR COREX FLOOR PROTECTION, CELOTEX INSULATED PLASTERBOARD, YOU CAN EITHER USE DOT AND DAB OR WALL PLUGS AND FIXINGS, HOPE THIS HELPS.

You can insulate the wall internally without the need to remove the wood flooring (leaving expansion gap is necessary),but you need to cut back the carpet after insulating the wall to make easy to replace the carpet in the future

Yes it is possible via a number of ways. You would need to fix a plasterboard with insulation on the back with drywall adhesive or with plugs and fixings. Also you could metal line the wall leaving a void for fibre insulation then fix normal board to metal or go tight to wall with metal and fix insulated plasterboard. Hope this helps.

Normally, you would have to remove the skirting boards to fix insulating plasterboards, and this can have a bearing on any carpets or woodflooring fitted, in that the walls would be further in by the width of the plasterboard and finish chosen. Alternatively, there is an insulating lining paper that can be used and would not cause problems of that nature.