Select 5V from PIC needs to be 3.3V I think
CLK 5V from PIC needs to be 3.3V I think
Yup. You should use more than just a series 1K resistor, though.
You could use a voltage divider on the 5V PIC outputs...say 2K series/3K shunt to gnd. That should work ok at slow speeds.
You could also use a pullup resistor to 3.3V and drive the outputs as open-drain, but that's not compatible with SHIFTIN.

Data 3.3V from MAX should be OK
For the input pin be sure to pick a pin that has TTL level inputs (PORTA and PORTB) and not ST levels, otherwise the 3.3V output from the MAX won't meet the input Vih spec.