I haven't got the correct BS spec in front of me now, but
yes I think its based on the root diameter of the thread as
that would be conservative for design calculations.
In fact all the design calculations relating to tension that I have seen are based on minimum root diameter.
In general, twice the shear stress is equivalent to the stress intensity, though that definition might not be quite correct. The stress intensity is limited by the yield stress and hence most design codes limit the shear stress to half the yield stress. I'd check with a design standard on correct factors to apply.