PIC, SPI problem with SD card and other devices
[...] pull-up resistor(10k) on SDI(MISO) line. With it SD card works good, and after initialization i can remove it and the card keeps to work, so i think the problem is really only during card initialization.


The SD card pins will operate in "open drain" mode after power-on. They need a pullup to output "high" until you switch the card to SPI mode.


  Anyway, this create another problem... if i use a pull-up resistor on SDI line, then the MCP28S08 can't read the correctly value of GPIO port. 


A 10k resistor will draw only 0.33 mA at 3.3 V. SPI outputs should be a lot stronger than that. You could try a bigger resistor, around 47 kOhm for a start, but you might need to lower the initialization frequency for your SD card.