With regards to 1, I wonder: why would calculating the Hamming distance be slow? In python you can easily do it like this:
hamming_dist = bin(a^b).count("1")
It relies on a string operations, but takes ~1 microsecond on an old i5 7200u to compare 32bit numbers. In python 3.10 we'll get int.bit_count() to get the same result without having to do these kind of things (and a ~6x speedup on the operation, but I suspect the XOR and integer handling of python might already be a large part of the running time for this calculation).
If you need to go faster, you can basically pull hamming distance with just two assembly instructions: XOR and POPCNT. I haven't gone so low level for a long time, but you should be able to get into the nanosecond speed range using those.
If you need to go faster, you can basically pull hamming distance with just two assembly instructions: XOR and POPCNT. I haven't gone so low level for a long time, but you should be able to get into the nanosecond speed range using those.