The field is infinite; it expands as you move through it. Of course there could be a mini-map showing a fixed area surrounding the viewport. This would add technical complexity, requiring the client to save an additional scaled down copy of each drawing to the db, but it's possible.
You can change the size of the eraser/brush with the palette that appears when you click the color rectangle. Perhaps this isn't obvious. Or did you mean that the maximum brush size isn't big enough?