Where can I learn to know that it overload the processor
On virtually every discussion of the Arduino it is mentioned that the current limit on the output pins is 40mA. Failing that the data sheet for the processor.
The ULN2803 is able to sink up to 500 mA per channel
Yes but you can't use all the channels at the same time at 500mA only a total of 650mA can be switched at any one time for any one chip. See:-
http://www.thebox.myzen.co.uk/Tutorial/Power_Examples.html
1 for each DotMatrix right?
No you only want to drive the rows with them to stop them from overloading the processor.
The point is that the simple circuit you saw is not the full story I think you have a lot to understand before you can embark on this project. Start off simple with just one matrix, there are plenty of tutorials to show you how to do this. Then only when you have that working think of expanding it. Look in the playground.