Can the SPI pins of an Arduino be separated from SPI? Are the SPI pins on the ICSP header of an Arduino Uno "separable" from the correspondent I/O pins - when one chooses to the use the ICSP header can the corresponding I/O pins be used for something else?
No.  Those pins are not separate on the microcontroller itself.  If you need to use SPI and still need more pins you may use analog inputs as digital inputs or outputs.  Otherwise you'll probably have to use an expander of some sort, or use a Mega or Due for additional inputs or outputs.