My pedal is slightly different, but the squarish white thing is the cartrige for a stack of carbon disks. The battery like cylinder with a wire out of each end is the capacitor that often needs replacement as the decades go by. They can cause speed issues, machines to run by them selves, blow up with a bang, or just make it all stop running. You can simply remove it and see what happens. (I kept it and showed it to a repair guy and he found a new one). My 730 has the large green metal pedal, my 900 Nova has a round pedal and the carbon resistor is just a tiny solid square bit. I think you might have the type with one or two stacks of carbon disks.
For speed adjustments you usually try different settings, and the idea is to get an even movement of the parts that move in and out of the cartridge (I'm not sure if its the correct terminology). When you press the pedal all the way it is suppose to touch the copper conductor parts directly and bypass the carbon disks. The carbon cartridge slows the current and it gradually increases speed as the pedal go down. From the picture I can't see exactly how it works with the spring action and adjustment nut, but push the pedal and observe how the mechanics work. The game is to find the spot (simply turning the nut to a different position) where the speed gradually increases and as the pedal comes fully down it obviously reaches full speed. I'm not sure if the explanation helps, but it is usually not too difficult for a DIY adustment. On the motor there's a switch for one even speed and another for gradual speed. Make sure you are not testing the pedal on the even speed setting, it should be a nice medium-slow stitching pace however far down you push the pedal. I'm probably just rambling on with all the stuff you know well and are onto already
Is it an original pedal? Berninas can be fuzzy with replacements, even with the basic pedal like this I know some have needed to get both a second and third replacment before it worked. In theory it should be fine, but it's one of those odd things that's happened more than once and I guess that's why some go for the more expensive Bernina brand replacements.