1) Which BT GPS receiver is available in India with SiRF III chip?
See if you can get one from US. I havent seen any BT GPS SiRF III for less than Rs 5.5K here.
GPS in India | Main / Vendors browse in addition to satguide.
2) Which map/software provider (using WM6) covers rural India and let me add my own routes?
mapmyindia has 2 options - iNav connect and iNav loaded.
MapmyIndia - iNav : Mobile Series GPS Navigation
If you have GPRS on your phone, after you have bought the GPS BT device, I suggest you try out the 5 day trial offer on iNav connect in order to check the accuracy of the maps available. AFAIK, they have fantastic coverage of even small rural roads but accuracy is doubtfull. Also, I doubt whether it lets you add your own routes.
Other than mapmyindia, I dont think there is any other option at all for rural India.