Your transcript quote does not mean climbing/descending confusion to me. The first question was about the altitude itself, not rate-of-change (remember, the plane was required to maintain a specific altitude). The second question might have been trying to distinguish between pressure altitude on the altimeter and GPS altitude from satellites, that's not clear. The third sentence shows they knew they were descending.
The ground speed given by GPS differs from the airspeed, due to the winds, and these can be very strong up there at 35,000. However, it might have provided some rough guidance if they had any decent wx info on winds at their altitude.