To try and answer this query:
1) With modern radars, the modulator within the TxRx will start to fire within seconds of being switched on (unlike to old 'RCA' type which took an eternity).
2) Darn good idea to use ALL of the time while operating the A/C.
3) Assuming you have EGPWS fitted, PREDICTIVE Windshear Alert is generated by the radar. (Again, assuming that this is modern Bendix/Honywell kit). REACTIVE comes from the EGPWC.
4) GPS/EGPWS is running full time; there 'aint an On/Off switch. (Just Gear/Flap O/Ride switches in many installations).