#1
I googled this, but did not get any definitive answers.

What kind of springs are generally used for fast double bass playing? You know, 16th note dhrrrrrrrrrrrrrrrrrrrrrrrrr type stuff, Amon Amarth type.

Would shortening the distance between the beater and the drum and using stiffer springs require less physical strength, or increasing the distance while keeping lighter springs be smoother?

Pedals in question are chain drive ones, with a single spring on each.
#2
I think you need to try some springs yourself and play with the beater distance until you find a combination that works for you.
There really isn't a "rulebook" to my knowledge. Someone correct me if I'm wrong.
Harmony: Stratocaster
Alvarez: F-200
Schecter: Omen 6
Fender: BXR-60
Dean: Metalman Z Bass (Betty)
Egnator: Tweaker 15
Pearl: Maximum
ESP/LTD: EXP-300
Custom: Harley Quinn Bass
Custom: TK-421 Explorer
A steadily growing supply of pedals
#3
In my own experience, tight springs and what i guess you could describe as a moderate beater throw length work best for doing double bass. With the springs too loose, I found the boards had too much bounce to them.... and with the beater closer to the heads, i ended up with a lot of unintentional double strokes because of the beater slapping back against the head. You can also lose a bit of power with the beaters closer to the head. At the end of the day, however, pedal tension and beater throw (like most things related to kit setup) boil down to personal preference. Just keep messing with your pedal setup until you find something that works for you.
#4
Having a setup you like is important for the comfort of playing, but the speed comes from technique. I have had hundreds of debates with other drummers about spring tension, board height and beater length, and in the end we all agree that everybody is different.

Find a technique that is comfortable for you, i.e heel-toe, slide, constant release, and work until you get up to the speed you want. It will take you years of practice but if you stick with it you will eventually get there.

I will also tell you that I am very limited above 160bpm or so. I have tried every different technique and have never been able to get the speed I really want. It definitely takes patience.

Good Luck.