Can I use TIMER1 instead of TIMER0 for FreeRTOS kernel and use TIMER0 capture interrupt for demodulation of signal present on CAP/EINT pin (resolution 8us)? How will this affect freertos functionality?

I have no idea which processor you are using, but generally you can use any timer you want.  The timer has to be able to provide a periodic interrupt of the frequency you require, thats all.  See the function prvSetupTimerInterrpt in port.c for the mcu you are using.

Just seen the thread title :-(