I'm a total newbie on electronics in general so forgive the silliness of my questions.
I've carefully hot glued two wires on these pins
You're kidding, right?
and put them into my arduino mega pin 0 and 1 (RX and TX), then I've opened the NewSoftSerialTest sketch, modified the second line
You've got An Arduino with 4 hardware serial ports, yet you are trying to misuse NewSoftSerial to perform software serial IO on a hardware serial port. Why?
NewSoftSerial doesn't work on the Mega. Unless you have the modified version, which then only works in certain pins (not including any pins connected to hardware serial ports).
The gps receiver gets power out of its own battery (3,7v Nokia battery) while the arduino is powered by my laptop usb port, so the tx and rx wires are the only connection between them.
Well, you need to glue a ground wire onto the GPS and connect it to the Arduino ground pin.
am I making things too simple by thinking that just hooking the gps chip TXA and RXA to arduino's RX and TX would do the trick ?
- do I need to connect the arduino and gps receiver grounds together ? (actually it was one of my tests, but when I did that I got a sync error from the arduino software when loading the code)
Yes. You'll need to disconnect anything else from pins 0 and 1 in order to upload code to the board.
- do a gps receiver usually send out serial messages while trying (and not succeding) to get a satellite link ? I'm asking this because all the tests have been done in a office room, with no clear path to the sky, and the receiver had probably not been able to get a satellite link.
No. Take the thing outside.