Any question answered...

Front brake caliper has had new brake cable/outer and it is tight as you like but it still pulls a bit extra after the pads touch, the housing moves a bit also.

Why?

Hope this helps
IMG 1633 - YouTube

1.Caliper arms twisting to accomodate disparity between the rim and pad parallelism.

1. Too much slack between the two caliper arms on the retaining stud, this needs to be a medium between being too tight so that the arms do not move freely and too much where slackness is introduced into the braking mechanism/action.