What do you mean by across power and ground pins
One end of the capacitor is on the power, 5V pin of the chip and the other end of the capacitor is on the ground or 0V of the chip.
why is it needed?
http://www.thebox.myzen.co.uk/Tutorial/De-coupling.html
These things are NOT optional in the real world.
Also why have you got a separate reset pin for each 4017 chip? One Arduino pin to all three chips is all you need.
You need to look at the data sheet for the 4017, you are using the Q0 pin, you don't want to do that, look at the timing diagram in the data sheet. You need to be using Q1 to Q8
The other thing is that you need a source and a sink to light an LED, this would mean inverting the outputs of one of the counters.
I think it is time to go back to the beginning and design it again. Maybe see:-
http://www.thebox.myzen.co.uk/Workshop/LED_Matrix.html