1) If you use BEDMAS: Brackets, (forgot what E was), Division, Multiplication, Addition, Substraction, I would do the 100/5 first. Then multiple that by 2, then add 2. So far, you have 24 inside the first brackets.
Next, multiply that by 100. The following 100/100 is just 1, so you can get rid of it altogether. Currently, you have 2400. Divide it completely by 50, you get 48. Then add 2, you get 50. The following 100/100 is also 1, so get rid of it.
Overall damage = 50.
I don't see where you got 8402 from. :x
2) I'll do the same with another random example off the top of my head.
((((2x85/5+2)x70x100/80)/50)+2)70/100)
So, it's 85/5 = 17. That times 2 = 34; then add 2, you get 36. Multiply it by 70, you get 2520. Multiply it by (100/80), you get 3150.
Divide it by 50, you get 63. Add 2, you get 65. Multiply it all by (70/100), you end up with 45.5
Overall Damage = 45.5 = 46.
The formula does work, if you do it in the right order.
Btw, you're missing "STAB x Weakness/Resistance" It comes right before the Random Number. Unless STAB is 1, and your opponent doesn't have a weakness against you.