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Dear Daniel,

to give the corners of an array, some "matplotlib" plotting functions have the "extent" keyword, e.g. "contour" and "imshow". You can use this to put your data on the map. However, the functions of the "Basemap" class do not support this functionality. "Basemap.imshow" overwrites the "extent" keyword (see docstring). A workaround is to call "matplotlib.pyplot.imshow" instead, to draw on your "Basemap" map:
>>> map = Basemap(projection='...', ...)
>>> map.drawcoastlines()
>>> extent = reduce(lambda x,y: x+y, map([lon0,lon1],[lat0,lat1])
>>> matplotlib.pyplot.imshow(data, extent=extent)
You can also create an axes instance first, to have more control over your plot.

To your second question: Since the real globe is a 3d sphere with longitude and latitude and your image is a 2d map with x,y coordinates, you need some rule how to transform longitude and latitude to your x,y system. This rules are the different projections. The main idea of "basemap" is to help you with this projection by calling "x,y = map(lons, lats)". So, I guess your are using "basemap" wrong, if you have to change the coordinates *by hand*. If you need more help, you should give a small example where your problem occurs.

Best Regards,
Gerrit