WRonX:
To answer your original question about multiple LCDs take a look at this thread: http://www.arduino.cc/cgi-bin/yabb2/YaBB.pl?num=1265969050. Scroll down and look at the pictures. This implementation is much easier than your shift register proposal, it's almost trivial.
I always was wondering, if it is possible to make "printScreen" from lcd,
This is not supported by any library that I have seen nor by the LCD controller instruction set. You could write a program to do this, but Mem's solution (maintain a copy of sent characters in your sketch) is much easier.
or just read the character on [row, column]
All of the above applies here too.
As Mem also stated "Usually it's a status bit that is read from the LCD ...". You can also get the last address that was used (or maybe it's the next address that is going to be used) when you get the status bit.
You can also use any of the 80 bytes of CGRAM (the locations where the displayed characters are stored) as general purpose RAM. This seems absurd nowadays, but when this device was developed RAM was very expensive and every byte was valuable.
Don