What are the advantages and disadvantages of the MiG-29's horizontal stabilizers (not what do they do)?
There is nothing too special about the MiG-29 stabilator.
The &quot;slanted&quot; (swept) axis of rotation is fairly common: as far as I remember, all MiGs that had a stabilator had this arrangement.
This has primarily structural advantages: it is easier to integrate the shaft (or axle) along the structural elements of the stabiliser, making it lighter. Also, the hinge moments are more consistent along the shaft. (For the straight shaft on a swept stabiliser, there will invariably be twisting forces that must be absorbed by the structure. Say, the root section may experience positive moment with respect to the shaft while the end section may have negative moment).
Also, as Charles already noted, a swept axis may allow to move the stabilator a bit further back (while keeping the same overall hinge moment), increasing its lever arm and thus efficiency. This is because the attachment point at the root can be closer to the leading edge. But this is only a gain when the actuator cannot be moved further back for some design reasons (like on MiG-29).
On the other hand, the leading edge may interfere with the fuselage when deflected, necessitating a &quot;stump&quot; at the root (which you can also see on most jet MiGs). At the same time, you need larger deflection in order to achieve the same aerodynamic effect (see also this answer).
The perception that the shaft is too close to the leading edge is a bit of an illusion. In fact, it is just a bit forward of the 1/4-chord line: exactly where it should be, as can be seen in these diagrams.