Your questions about the Inmarsat receiver's capabilities are valid and are similar to mine.
I have a friend who is a very experienced RF engineer and I've spoken with him several times about this question of the Inmarsat data. One possibility is another Inmarsat satellite with overlapping coverage had record of fl-370 engine communications.
Another possibility is that every logfile of 777 engine reports in which positional data was also reported was compared against fl-370 engine reports. Inmarsat engineers may have then been able to determine that based on speed and direction, the received signals would have certain characteristic phase (Doppler) shifts.
http://theconservativetreehouse.com/2014/03/28/mh-370-back-to-the-drawing-board-all-prior-search-areas-abandoned-with-new-search-area-established-684-miles-further-north-east/-—————and then this....http://theconservativetreehouse.com/2014/03/28/mh-370-the-maldives/