I have M. nigra thriving on neutral dry soil full of stones in SE England. My mother has both M nigra and M alba thriving on damp alkaline clay in SW England, where they grow faster. The famous mulberry tree at Merton College Oxford allegedly planted by King Charles I about 1645 is on clay. They are widely grown as a street tree in Mediterranean places, where they are pollarded back to a branchless stick every year. I think you don't get any fruit that way, since the flower buds form on last year's wood. In sum, I don't think they are very fussy about soil. Not heard of them suckering, perhaps that is M. rubra.

They are very late into leaf, not until May even in Crete. A hard frost in April will kill off all the buds and set them back, you'll lose the fruit that year. M nigra and M alba are monoecious, it is M rubra that is dioecious.

M nigra isn't as hardy as M alba and M rubra, and needs sufficient summer heat to harden it off to survive the winter. It is easy to grow in much of England, but uncommon in the north and Scotland.