I think Fuzzy IBE should work, but there is no notion of "proportional" : you can totally decrypt if your identity is near (in the sense of Hamming weight) and you can't, if it is not the case :
Yes, it is possible to encrypt a BMP image with any stream cipher.
First of all, you need to cut the first 54-byte of the BMP image into another file. At this point, the data part begins. Then the rest can be encrypted with any stream cipher. After that prepend the header to the encrypted file.
Here the example with OpenSSL. I will use AES with CTR mode ...