There are a few engineers that visit this forum one of whom is far better qualified to answer than I but as he hasn't I'll suggest some possibilities for the technical parts. Question 2 is best answered by my ATC colleagues.
Within the UK we have had similar incidents since the new Mode S ground interrogators entered service. The problem in the UK is caused by some aircraft transponders provided incorrect responses to the ground interrogations. Typically this shows as an aircraft with a 7000 Mode A code operating around 2000 incorrectly supplying a Mode C response between FL180 and FL210 to the Mode S interrogators. It continues to provide the correct Mode C response to the older Mode A/C ground stations. That could be what is happening here but the details supplied about the radars in use are slightly confusing and the SSR radarbloke is using would have to be a Mode S interrogator. If it's 12 years old it probably isn't but that might just be the age of the whole system and bits of it may have been upgraded since. In the UK these corrupt responses don't show up on TCAS in other aircraft which continue to see the correct height.
If this is what's happening the only way to stop this is to ask the aircraft to switch off its transponder. Just switching off its Mode C doesn't work as we have seen cases of this happening with aircraft which are not Mode C equipped. It's an ATC call as to whether they prefer a label with a corrupt response or no label at all. There may be some conflict between the controller of the higher airspace who probably wants it switched off and the controller who actually has the aircraft in his airspace and a lot will depend upon whether or not either controller is using height filters and whether the rogue return is in conflict with anything..