Stairs creaking could be:
1) Detached risers due to gripper rods being hammered on the treads - builder will claim defect caused by your carpet contractor.
2) Insufficient fixing of loose components at kite winders, half landings in the flight. They should have been glued and screwed by site carpenters using blocks supplied with staircase. Removing the plasterboard under the stairs will reveal.
Landing.
1) Probably made worse by central heating and mains pipework coming form the airing cupboard.
2) Floorboards need taking up to inspect and diagnose. Could be trimmer, joist spacing, hangers, or the flooring itself.
Finally, I would suggest your original carpet contractor relays the carpet as it will need re stretching.