I'll take them in the order asked
1) The crossing is generally only monitored during raising and lowering of the barriers, although the signaller can call the picture up at any time.
2) There is an "Up" and "Down" indication for the barriers.
3) The signaler can't clear the protecting signals unless the barriers are down and he/she has pushed a button to confirm that the crossing is clear. There is a recent development at some crossings where the verification that the crossing is clear is done by obstacle detection technology.
4) The operator makes the decision as to when to lower the barriers, although some locations automatically do so. There may also be an indication as to when to lower the barriers to minimise "road closed" time.
5) The signaller will be able to monitor approaching trains by occupancy of track circuits, essentially, as you put it, "live tracking".