becuase the fabric you have selected is a light background and the current fabric is a solid dark color
ahem
I would suggest removing the old fabric....unless of course it wont bleed through the new fabric...both in visual and well...you know..beer stains and all that.
Ive done both...removing and go over...all depends on the fabric at hand and the fabric in place and the state of the cushion.
Regarding the plywood...regular size/width? Just as in nailing I would go with a standard length not to protrude past the plywood but to also keep a strong bond.
I would also suggest that if you will not be finishing the edges of the fabric, you might want to run a little hot glue so as not to fray/rip etc later on when you've sat in them a while.
And, my final suggestion would be to start on the length and finish on the corners, pulling tight.