Usse the extension->render-.grid to set up the grid on the canvas.
Have the grid layer abover the layer you will be drwing on.
Use the bucket tool being sure the layer that is active is not the grid layer.
Point the buket fill in each grid you want filled.
The bucket tool can be dragged accross multiple gird square and they will all be filled.
To move the canvas to the left or right hold the Ctrl key down and use the arrow keys - in window.
To round or squaare corners in inkscape - take the small circle in the upper right corner and pull down or up.
If it is in the upper right position the corner will be square.
If it is along the edge on the top or right side the corner will round to that point.