Another location given on northern broadsides was Maxwell Town in the Scottish Borders and this may have been the original as I don't think Maxfield exists. Maxwell to Maxfield to Mansfield may have been the progression. There are 3 localised versions in The Holme Valley Beagles song book.

The song is very likely a generalised piece as such songs often mention several place names and personal names whereas here we have the setting and a Jemmy and a Tom.

I think some form of albino is the more likely as in the song it is treated as a one off, whereas if it was a hare with a winter coat there would have been several such.

'The number of dogs' etc. has to be seen in context of the full 2 lines.

The number of dogs they never could be found, nor never better hunting upon the English ground. The word 'better' is to be applied to both things being described, in other words it's glorifying the pack and the hunt itself.