Can't comment on the cable pull issue but from the top photo I can tell you that you've got the brake blocks badly mis-aligned. The block on the left looks to be canted downwards and the block on the right, a little upwards. This would mean they aren't contacting the braking surface square on, which would cause a spongy feeling and lack of power. The easiest way to align them to the rims is to loosen that bolt and stack of washers and dished spacers, then hold the brake on and wiggle the block until it finds its position sitting fair and square on the rim then begin gently to tighten the holding bolt until everything is tight. Your problem here will be that the torque that you put on the bolt will tend to pull the brake block out of alignment so pressure from the brake lever and holding the block with your fingers to prevent it from rotating will be needed. Another hand to hold the brake on might help, or I suppose you could use an elastic bungee wrapped round and round the lever and grip. Get the blocks so that there's a millimetre or so of clear braking surface above and below them because they are tapered and will need more width as they wear.
This might take several attempts to get right but in the end you should find that the brake blocks are both at the same height in those slots and look symmetrical when viewed from behind.
Next, adjust the little spring tension screws at the bottoms of the brake arms to get both brake arms standing up parallel. Tightening the screw increases spring tension.
Then adjust the cable length to get the blocks the right distance away from the rim. When you grab the brake you should hear the blocks contacting the rims with a little "clack". If the above doesn't improve things dramatically you have a cable-pull ratio problem and I can't advise you.
If the bakes squeal when applied, repeat the alignment exercise but toe the blocks in by trapping a twice-folded cereal box lid flap between the rim and the trailing edge (rear) of the brake block then tightening everything up.