So I dropped it into maptool to see how this works. I assumed a grid size of 100px as that fits nicely with the top right room - but you can see that the grid doesn't really work well as soon as you move away from there. Ideally on something that looks as rectilinear as this - you want the walls to run along the grid lines.

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As for doors - you can place them in the base image or have them placed later. It doesn't really matter one way or another. I do think that it's worth having a little colour on the ground outside if only to place the map in some form of context.