>Does the CCS compiler runs with ICE2000 under MPLAB ?
>
>If so, does it provides C source level debugging ?


Take a look at Microchip mcc18.
Microchip mcc18 runs with ICE2000 under MPLAB and provides C source level
debugging.
There is a difference with asm when you are debugging C : mcc18 store local
variables in a software stack located at 0x500 so to see them you will have
to look at the 'file registers' window.
To see C global variables just open a 'watch' window.
Mcc18 is not free, but you can download a demo version from microchip

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