Can impact events cause widespread volcanic activity on the other side of the planet?
Note: this is a part answer, based on recent research and modelling

There has been considerable research recently in what is known as antipodal disruption, in particular, a group from Princeton University have produced a model that overcomes the main deficiencies of commonly used models that have the Earth as a 'featureless sphere' (1)(2).  Simulations using a symmetric spherical Earth produce a deceptively large peak at the antipode (2) - this is often cited as being some form of proof for the P-T example that you provided in the question and an antipodal relationship between the Deccan Traps and the Chicxulub crater (1).

However, the Princeton team's simulation (1), (2) show that there ought to be an antipodal effect, but when the elliptical shape and the heterogeneity of the surface is taken into account - where the waves end up and their displacement when they get there are quite different to the spherical models (1), to the order of 4 times less displacement and the antipode effects are not on a point source (2).

This results in a disagreement with the Deccan Traps-Chixculub relationship, as shown in the late Cretaceous model below, from (1):



This has implications for not only seismicity, but for volcanism and hot spot activity, due to the modelled impact seismic waves (across the surface and through the Earth) showing to be unfocused and scattered, this results in less severe ground displacement, tsunamis, and seismic and volcanic activity than previously theorized. Their models showed that the antipodal region had 'chimneys' of peak stress, strain and velocity.

Meschede et al. 2011 (2) conclude from their model that there would be greater seismicity in the region around the antipodal 'chimneys', this increase in seismicity can trigger volcanism, and even though the impact energy has been modelled to be insufficient (by several orders of magnitude) to induce melting to form an antipodal hotspot.

Some ongoing research by Hagstrum, 2005 (3) has suggested that oceanic impacts may result in hotspot/large igneous province antipodal pairs, this is due to, according to Hagstrum, oceanic crust having a greater seismic efficiency that continental crust. The mechanism is, according to Hagstrum,


  an
  inherently antipodal mechanism of hotspot formation
  is proposed in which one hotspot forms at an oceanic
  large-body impact site and a second hotspot and
  possible LIP are formed from seismic energy focused
  in the lithosphere and upper asthenosphere at the
  impact’s antipode.


However, it is not clear if the non-spherical heterogenous nature of the Earth's lithosphere was taken into account, given that, as stated, the impact energy is insufficient to cause melting, Ivanov and Melosh (4) state that the seismic mechanism may contribute as a trigger for a "pregnant" hotspot to activate, not through melting, but through increased seismicity (fracturing rocks etc).  

(Note, the use of "pregnant" is their words, not mine) 

Conclusion

The models created by Meschede et al. (2) have found that it is theoretically possible for localised antipodal volcanism to occur, but this volcanism would not necessarily be the direct result of the impact itself, but due to the contribution of an increase in antipodal seismicity (increased earthquakes fracturing rocks in the lithosphere etc). 

Meschede et al. (2) contend that their model indicates that the impact energy is very much insufficient to result in a sustained mantle plumes and hotspot volcanic regimes as in the previous models.  However, there is still ongoing research about the impact energy contribution to the formation of hotspots and 'traps', particularly for oceanic impacts (3), but this is very much uncertain (2) and unlikely to be the direct cause (4).

References

(1) Kelly, 2011, Impact study: Princeton model shows fallout of a giant meteorite strike, News at Princeton, Princeton University

(2) Meschede et al. 2011, Antipodal focusing of seismic waves due to large meteorite impacts on Earth, Geophysical Journal International

(3) Hagstrum, 2005, Antipodal hotspots and bipolar catastrophes: Were oceanic
large-body impacts the cause?, Earth and Planetary Science Letters

(4) Ivanov and Melosh, 2003, Large Scale Impacts and Triggered Volcanism, in Large Meteorite Impacts