Re: Is the map of Mars that Giovanni Schiaparelli drew correct?

The answer to your question is "sort of". While I hate to sound like I'm running for office, it depends on what you mean by "accurate". The maps of Mars made by Schiaparelli and others were certainly quite good given the telescopes of the time. But they often also saw details that were not really there, as well. Schiaparelli is, as you may recall, the person who first claimed to have seen "canali" (Italian for "channels") on Mars's surface. Later, Lowell also drew maps of Mars showing canals which he was convinced were there. So you should not believe everything you see in their maps, but as you can see, they also were not incredibly far off.
Here's a map drawn by Schiaparelli:

And here is a map drawn by Lowell, along with a photgraph of Mars. Notice that they looked a lot alike, if you ignore the "canals"

(figure borrowed, with permission, from The Cosmic Perspective by Bennet, Donahue, Schneider and Voigt)
Modern maps of Mars, or of any planets, are a lot more accurate thanks largely to our spacecraft images. But the fact that these men drew their maps by hand based on staring through a telescope in a cold observatory night after night should make us appriciate how dedicated they were and how remarkable their work is.
Hope this helps!