I personally do not think that it would matter for my problem.
Yes but it would make other people understand what you are doing a lot better.
Sorry I don't know where you got that design from but it is very wrong.
First of all there is no current limiting components, a resistor is the simplest way of limiting the current.
Next you can only light up one LED at a time. This means that each LED is only on for 1/64th of the time. That means it will be very dim, remember you do fading with PWM by adjusting the on / off ratio.
I really do not get how leds that are in LOW@ +ve terminal and LOW@ -ve terminal can have any current passing through.
Yes you are right about this.