are the sentences correct?
* pins 0 and 1 do not work when the Arduino is connected to the computer, because then the serial communication is working through the USB port.
No, this is not right. Pins 0 and 1 DO work - they perform a specific function, though, so that they are not available for other purposes.
*if no additional library is used, pins 0 and 1 don not work for serial communication
No, this is not right. The HardwareSerial class, instanced as Serial, is what makes pins 0 and 1 work for serial communication. That library is part of the Arduino core.
As I am using 1.0 the library to employ is SoftwareSerial.
Yes, this is correct.
Then I will be able to communicate to the modem.
Well, that's a big leap, but, in theory, you should be able to.