Hello Yungao,
1) Yes, this is supported, you can find more details here:
http://linux-c6x.org/wiki/index.php/GDB
2) Yes, however, I would strongly recommend a low cost EVM. E.g.,
TMS320C6678 Lite Evaluation Module only costs $399
http://www.ti.com/tool/tmdsevm6678
3) Please try with the GDB instructions on 1) and let me know if you really have this issue or not.
best regards,
David Zhou