Relation between SPI, clock rate and data bits in microcontroller
SPI uses synchronous communication, i.e. the device which originates traffic (the master) sends clock to the slave. As long as the clock rate is not higher then quarter of sampling frequency at the slave, any frequency can be used.

Architecture of communicating processors has no significance, if both sides can work with same word length (all should be able to do 8-bit SPI).

What has to match, is the SPI mode. It describes clock polarity (CPOL) and clock phase (CPHA). Most common mode is 00 (clock idle low, data out at falling edge, data in at rising edge).