Gums: it is a 2-way system by design and you are right on with your understanding. Data, including FLT PLAN and PERF DATA can be uplinked and downlinked to/from the FMS, however uplinked data will not become active until reviewed and EXEC'd by the flight crew.
Every 30 mins: On the 777 and most modern Boeing aircraft, downlinked reporting frequency is entirely controllable via the FMS CDU. I am unaware of a normal timing standard, but 30 minutes seems reasonable. Typically the minimum reporting points for a block would be OFF STAND, AIR/GROUND=AIR, AIR/GROUND=GROUND, ON STAND.