If the gearbox shifts down when it heats up, if there is a backoff, the gearbox must be opened, but the gearbox must have been used very badly to give this fault, or the km is not original. There are linings between the oil filter and the gears inside the gearbox, besides, it loses performance over time in the turbocharger, the system will return to its healthy state with a medium revision since it changes in the valves in the gear system.
The event you experience in 2nd gear is normal, if you press the throttle a little while driving at low speed on a straight road, the vehicle will increase speed without downshifting and continues to accelerate and then goes into 3rd gear. This event is present in all transmissions.