The stump which is a horse chestnut was chopped down about 2 month ago, it
is about 15 inch in diameter, if I dig round it how deep will I heed to go
before I reached the roots, and would I need a axe or a chainsaw, and could
I lift
it?

Could I burn it out by using charcoal or coal, petrol any thing like that

or use http://www.daxproducts.co.uk/rootout.html