As for brands, Automotive love microchip and atmel eeproms, (now the same company),
As for your actual errors, Its almost implying an error in your code, or your expectation of how the device expects data,
Most of these eeproms can operate in either an 8 bit or 16 bit addressing mode. This doesnt seem to be the case but i would check it,
Most of your weirdness is that for lines 0-1, 2-3, and 8-9, A-B your getting a half line error, are you 100% certain you dont have an error on certain values in how your addressing the memory,