Lime mortar

Yes you can use natural hydraulic lime below the damp proof course. This is done often on more gentrified projects because there is so many reasons to use lime mortar over portland cement, from health reasons to structural and longevity.

Natural hydraulic lime (or NHL) comes from limestone that has natural impurities of clay and other minerals, the amount of impurities within it determines how hard it will set so I don't see why you shouldn't use it on a new build as long as it's done correctly and not against any building regulations i.e vents, tried or weep holes.

No, you should use NHL 5 below the dpc due to its higher strength and lower permeability then NHL 3.5.

no