Would anyone know, is the chance for a knock down with the perk Super Slam a fixed percentage or does a higher critical chance increase the frequency?

Don't think having a higher critical chance will increase the chance of a knock down, but I think it's possible scoring a critical hit may increase the chances that a knock down with Super Slam will occur. So in that sense it may increase your chances.

Wish I knew myself what governs/affects Super Slam. For example, does a power or charging attack increase the chances of a knock down? Are more powerful hitting weapons or weapon class (like a Super Sledge, or two handed vs. one handed) more likely to knock the target down or it is just a flat percentage on any melee or unarmed strike - if it is then a fast striking weapon (like a Combat Knife) would obviously do a better job of knocking people down.

Wish I knew the specific effects of some of the VATS melee/unarmed special moves. The special move for fast slashing melee weapons for example: Back Slash. This consumes less AP but does less damage - but is there anything else to it? Does this special move have an increased critical chance for example, or be more damaging to limb condition, or more likely to cause a stagger, or a knock down with Super Slam? I guess for a lot of things it's just a stab in the dark - left to the imagination and experimentation and observation. I wish things were just detailed so you knew without having to try and figure it all out by yourself.

From what I've seen higher luck does play a part in it but not by much.

Luck does contribute to critical chance. Dang, now I'll have to get off my duff and test this myself. I have a high crit sniper character that I'm working up the melee on. Once he has it maxed (so the test isn't affected by weapon skill differences) I'll make a low crit melee character and compare them.