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Given the 16bit Pearson hash of a 112 bit message, how many other messages have the same hash ?

What's the probability that a similar 112b message of a given 112b message (you can define similar however you want, for example so that no more than 1/4 of its bits have been altered) has the same 16bit Pearson hash value ?

For the second question, what would be the result if it was a CRC-16-CCITT (the polynomial is x^16+x^12+x^5+1) and a 8KB message instead (is CRC-16-CCITT a good checksum for messages of length up to 8KB) ?

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