Recently a friend donated a Silicon Labs C8051F devkit to me. It has this USB Debug Adapter. For me this device looks like a JTAG adapter or I'm wrong? Is it possible to debug other MCUs like ARM (Raspberry Pi rev2 specifically) or AVR with this USB device? And if possible which software to use with GNU/Linux or Mac OS X?
Yes. Your device supports JTAG. You need to use the Silicon Labs IDE. You can find the JTAG informations from here http://www.silabs.com/Support%20Documents/TechnicalDocs/8-bit-USB-Debug-Adapter.pdf
But the problem is that this module will only allow to debug Silicon Labs micro controller. For using this debugger with Raspberry Pi or other such devices, you need a separate software. This is currently not available.