I can not disclose details of what data we mods get, but I can tell you that it looks quite similar to what you found. Given that SE likely uses the very same data (probably together with those obtained from Google) this may not be too surprising.
The spikes are due to social media; see also here and compare with the dates on reddit. It is noteworthy that if you consider visitor counts average over seven days, all spikes caused the (before September) mostly flat visitor curve to rise sustainably. Apparently, visibility on social media does bring new regulars.
As for the reason for the latest increase, we can only speculate. Winter term started at universities and many questions seem to be study-related, true, but last summer term did not cause a comparable increase. Therefore, university schedules can't be solely responsible. People with more experience across multiple SE sites may be able to offer more.
Our traffic by search engines is still at only 60%; according to SE folks, that figure should in the nineties eventually.