I would also like to find out if we can link this mass extinction event to others, like the Permian.
No, the Permian mass extinction was almost certainly exclusively the work of supervolcanic eruptions in Siberia known as the Siberian Traps. There was cursory evidence of 'shocked quartz' in the continental strata of Australia/Antarctica suggestive of an asteroid impact from that time, but this evidence is challenged by its outdated methods of detection. Whatever the case may be, supervolcanoes don't seem to follow a pattern of any sort, aside from that of short-term tectonic shifts.
Are these super mass extinction events truly periodic and does the sun's path around the center of the Milky Way influence these events?
No, they are not periodic. If traced on a timeline, it may seem like events like these are superficially so, but in actuality the events have little in common with one another. The only cyclic extinction-level events may be those of large asteroid impacts, since one the size of the Chicxulub impactor (the one that finished off all non-avian dinosaurs) strikes about every 100 million years or so, one slightly smaller strikes at around 50 million years or so and so forth. These NEOs obviously orbit the sun like the Earth, and so have a cyclic nature in relation to our planet. The trouble here with this theory is that the vast majority of those asteroids and comets, even those of the size of the K/T impactor, are alone not enough to truly count as extinction-level events when they hit (though they ARE
quite devastating). To qualify as deadly, they need to hit in a particularly sedimentary deposit or shallow sea, and in sequence with other natural disasters which have already weakened the local ecology (during the Late Cretaceous, those were the Deccan Traps blowing some hundreds of thousands of years before the Chicxulub steroid impact).
Aside from that, it is difficult to say what may be cyclic and what is not in terms of extinction, since the overall fossil record, especially that which is older then 500 million years, is incomplete at best.
and does the sun's path around the center of the Milky Way influence these events?
Probably not as much as one would think, since the chances of the sun being in the danger zone of a supernova explosion or a gamma ray burst during its 250 million year orbit roughly on the galactic plane is pretty slim. That being said, there are various extinctions attributed to interstellar trouble, the
most recent of which is the Pleistocene extinction of 2.6 million years ago, in which a supernova 150 light-years away is possibly linked to the great dying of many Earth megafauna, especially shallow marine animals like the massive
Carcharocles megalodon shark. This dying off of the megafauna is attributed to increased risk of cancer (up to 50%) in those creatures from fast moving
muon particles released by the supernova. Smaller creatures seemed ansorb less of the particles, and thus escape harm.