If that's white cedar, there may be enough come and go to take up the 1/16th. If red cedar, seal it. Centerboards, despite their name, do not have to be on centerline as long as they are parallel to the major axis of the boat.

The fit on the stop should be snug but not tight or you will force the fibers apart.

Heartwood is good. It is the ideal when you go to the lumberyard and is often unobtainable because it has been sold to a higher bidder.

How narrow is narrow. Unless you are an experienced canoeist or kayaker, I recommend you don't go below 28" of beam. The touring canoe is 30" and is quite comfortable.