I'll preface the Archery topic with
this link that you might find useful.
When it comes to archery, what exactly makes the crosshair hold longer, power-draw or WPF?
For reticle-holding, WPF will always help. The more WPF you have, the longer you'll be able to hold. Power Draw over the requirement of the bow lets you hold the reticle for longer, for the most part.
Is WPF the sole responsible for draw speed?
In addition to the base speed of the weapon and WPF, Power Draw also affects how fast you can draw the bow. The higher the Power Draw, the slower the drawspeed; at least in my experience.
Is power-draw useful for requirements and extra damage alone?
As mentioned above, Power Draw over the bow requirement lets you hold the reticle longer (usually). Higher Power Draw also increases the missile speed of the arrow, giving it less of an arc and allowing for more distance over time. For the most part, this is extremely useful, since you don't have to lead a target as much.
Do athletics alone define how fast your character moves around? Do agility points have any influence here?
WaltF4 made
a study about this. The short answer is that Agility adds a small amount of movespeed per point, with Athletics adding more per point. Movespeed is also reduced by the total amount of weight you're carrying, and is further reduced by the specific length and weight of the weapon you have in your hands. You're also penalized for holding more than one shield.
Is power-strike solely responsible for melee damage? Does strength make any difference?
Strength adds a flat damage bonus after WPF and PS are taken into account.
Vargas' Toolkit has a good calculator for this, and should be up to date with the most recent armor soak/reduce values.
Hope this helps.