In my country, Nexus 7 2013 Wifi only tablets are still available. It comes with Android 4.3, but I was told that it updates to 6.0.1 (official update). Does anyone know if this is true? Also, is it stable on 6.0.1? And will Facebook, Instragram, Pintrest & Google Photos apps be stable on it?
Yes, it is true that Nexus 7  (Wi-Fi) can be updated to official Android 6.0.1. On Google's factory images page for its devices you can see all the updates.
The concerned apps work fine with Android 6.0.1, at least on my Nexus 6 with Android 6.0.1.