I know that these two (Wifi and Bluetooth) are in the same range of frequency (2.4 ghz. At least mine ones are this way).
I do not think wifi modules for embedded systems (I use AVR) are cost efficient, thus it would be much more better to use a Bluetooth module such as HC-05 to communicate with wifi access point. Is it possible? If it is possible, can you give a brief idea how can it be done. Thank you in advance.
It wouldn't make much sense as popular ESP8266 WiFi modules are actually cheaper than HC-05/HC-06 Bluetooth (less than $5). Example project connecting ESP8266 with ATmega32 using avr-gcc: http://tomeko.net/other/ESP8266/ . There are also many project based on arduino platform and ESP8266 can also work without external microcontroller making AVR obsolete in some application (if its GPIO pins number is sufficient, there is no need for ADC, etc.).
If you'd still like to use router as a WiFi access point than using ENC28J60 and connecting AVR to ethernet port of the router would be better idea than using Bluetooth.
No, it is not possible. While Bluetooth and Wifi operate in the 2.4ghz unlicensed spectrum, the two protocols are completely different. So different that they tend to interfere with each other, and spectrum sharing modules have been created to manage that interference. There is no way to get bluetooth to wifi without an intermediate device, module or computer.
