Chris,
No problem with flightsimmers - your questions are in the same ball park as those who play with the real birds and the answers should be of similar interest to the rest of the folk.
so now I imagine that I’m flying up against a wall
In the early days of compressible flight problems (WW2), the drag increase associated with approaching transonic speeds generated this concept of the sound "barrier". In reality, what we get is a drag hump transonically and then the drag reduces once you are reasonably well into the supersonic side (which is why we don't fly at or around M1). Not really a case of flying into a "wall" .. although it appeared that way as the thrust capabilities of the aircraft of the day were a bit modest for transonic flight .. which is why early experiments involved steep dive angles so that gravity helped out.
The other problems associated with handling tended to be associated with the movement of shockwaves and shock flow separation and were the real flight test problems until the boffins got their heads around what was going on.
the wall moves (relatively slowly) along the length of the aircraft.
Not too sure what you are thinking about here but let me have a stab at it.
At some stage (dependings on the aircraft design) you will get localised transonic flow in small regions of the airframe (typically just aft of the cockpit and somewhere near the thickest part of the wing).
As the aircraft speed increases, you end up with a shock wave as the local flow gets to the local speed of sound. This can produce significant flow problems unless the shape of the structure is designed to suit the flow requirements. There will be a small volume of supersonic flow ahead of the shock wave and the latter marks the surface where the flow transitions (quite abruptly) back to subsonic flow. An analogous situation is what you see in a sink if you turn the tap on hard - there is an outflow pattern from where the tap stream hits the sink surface and then an abrupt stationary water wave - this wave (usually referred to as an "hydraulic jump") is the equivalent of a shock wave.
As speed increases further, this initial shock wave surface gets bigger and moves back toward the trailing edges. At the same time the air molecules in front of the aircraft start to bunch up a bit and you get a bow wave (not unlike what you see ahead of a boat bow). Initially, this stands off a way from the front of the aircraft but moves back toward the aircraft as the speed gets into the transonic region.
As speed increases further the bow wave progresses aftwards until it intersects the sticky out bits of the front of the aircraft (nose, pitots, etc) and becomes attached to them. The "front" bump of the wave is referred to as a "normal" (ie at right angles) shock wave and is associated with significant changes in flow parameters (pressure, temperature, velocity, etc) while the slopey bits forming a cone are referred to as "oblique" shocks and have less of a flow problem. The early shocks on the aircraft move towards the trailing edges (often with quite a bit of jumping about) and attach there.
As the aircraft's speed increases supersonically through the transonic region, the flow patterns become stable and you end up with the nose shock wave and a trailing edge shock wave and the overall drag reduces to a steadier situation.
Other characteristics associated with the flow include
(a) the conical angle of the shock wave is related to the Mach number and is referred to as the Mach angle
(b) the "sonic boom" we hear about from time to time is what occurs as the leading and trailing edge shocks traverse a location. You get a rapid double pressure pulse and the characteristic "bang -bang" audio trace. The intensity of the sound depends on a bunch of parameters but, for supersonic flight at cruise level, the ground pulse signature is a fairly gentle doublet.
Eventually, this pressure wave is going to get very close to some important aerodynamic controls (wings & control surfaces)
.. and, if the design doesn't accommodate the supersonic flow and shocks appropriately, you are going to get severe flow disruptions, flow separations and all sorts of nasty pitching changes and generally deteriorating handling qualities.
What happens to the aerodynamics of the wing ..
Apart from the transition to supersonic flow, the main problem (handling related) is tied up with a general aftwards movement of the centre of pressure (net effective lift point, if you prefer). This leads to a significant increase in nosedown pitching tendency (pitching moment) and, if the aircraft is not designed for it, significant handling problems (Mach tuck). In the early days, a number of aircraft were lost as the dive was uncontrollable and led to structural failure. In addition, for subsonic designs, there is a high likelihood that the flow will separate at the shock wave and you can find your control surfaces in separation areas (ie useless). An alternative problem can see localised aftwards movement of control surface CP leading to hinge moments (tendency for the control to move one way or the other due to airloads) too high for the pilot to overcome (think of the pilot's control inputs as being intended to move the control surface and that this movement is resisted by the hinge moment - the pilot feels an increasing stick load and eventually, it all gets just to much for the pilot to push and pull as necessary to effect a movement).
until I start to feel the effect of the M2.0 wall approaching ?
I have no idea what you are considering when you refer to a "wall" around M2. Perhaps you are looking at the temperature rise associated with supersonic flow (an M^2 function so it ramps up rapidly) - generally we consider this to become a significant problem for aluminium structures due to structural weaking associated with increasing metal temperature. You will be aware that the high speed aircraft (SR-71 and similar) have all sorts of exotic materials to permit operation at these elevated skin temperatures.