Hello,

[*] Do the ECU store these data even after power-off, or do I need to transfer them to PC at the field?

No you need the a PC or netbook at the field.
[*] How long recording time will the ECU be able to store?

Latest version about 20 minutes. Older versions maybe 8?
[*] How do I get the data over to the computer? Do it exist some kind of serial or USB interface/software? Aprox price?

Yes it is a serial device. Some third party USB serial converters will work. US$125
[*] I read something about it measuring G's? Do it have a built in G-meter?

Yes it derives G forces from GPS data (2nd derivative of GPS position), not sure of the accuracy of such a system, especially with changes in altitude. In level flight it might not be too bad.
[*] I'm mounting this equipment in a CompARF Eurosport. Should I take any special precautions to placement of the GPS unit, or will it work wherever in the model, as long as it's facing upwards?

Looking towards the sky, the frequencies are at around 1.6 GHz, so treat the antenna like you would a SS receiver and keep it pointed upward.

Regards,