Is this library completely free?

Yes. It's completely free and open-source. It's a result of many efforts during last two years.

How could I install it?

Just unzipping the archive file in library folder present in the Arduino's root folder.

Where can I report an issue or a problem?

In this first step you can report an issue using the issue-platform of the Google Code site where the project is currently hosted.
After you will be able to report your experience in a forum dedicated to this library.

Which shield is completely supported?

This library is developed using GSM/GPRS & GPS Shield of Open-Electronics.org and futurashop.it.
We're working in order to make this library compatible with the TiDiGino board.
Other shield are not ufficially supported.

How can I switch between Arduino Mega and Arduino UNO/2009?

To switch between the two board you should comment and decomment appropriately the lines 2 and 3 in HWSerial.cpp.

How to enable debug comments?

Just decomment the line DEBUG_ON in GSM.h and reupload the code.

Still not any reply to your doubts?

In this case use the forum to report your experience.