Sorry to say I need a bit of hand-holding on this one.
3D: short walker about to mince briefly in stages (6)
Are we going with PED as the short walker, ie the answer ends in ‘D’?
16A: measure between sets of factories - it’s extremely close (7)
N_AR_ST
There can only be one answer - it’s the plural, ‘sets’, stopping me from fully understanding parsing, I think.
8D: Scottish corporations’ rumours to test public opinion (5)
KI_E_
Now this one I don’t understand. I’d be really grateful for a hint.