SD card v1.0 CMD8 command reply
1) Why 2Gb card behaves like v2.0?


Almost all 2 GB cards are newer than the 2.0 SD card spec, and thus support the newer commands. But they still run in SD mode - the 32 bit address is measured in bytes and not in 512 byte blocks. 

Only SDHC cards >= 4GB use 512 byte block addresses.


  2) What to do in this case?


Set the block size to 512 bytes and use the card as any other SD card.


  Where I made mistake in the init process?


You should use the elaborate SD card initialisation that is shipped with FATFS instead of trying to roll your own.