Do I need buffer amps and zeners for SPI pins in a tiny IC chip?
Opamps/zeners: no that is too complicated, what you need are levelshifters.

That can be in the form of a chip, some resistors (for 5 V to 1.8 V) or a transistor and a resistor (1.8 V to 5 V). You can also buy small ready-made levelshifter boards on eBay. An example.

or this one from Adafruit2