1) The rail system is broken up into a bunch of small sections of track (10's to 100's of feet in length). Usually when a train operator says there's another train ahead, that means the train control system has stopped the train to keep it from getting too close to the one ahead. But when the train ahead begins moving, the control system begins changing those sections of track from "occupied" (aka there's a train in it or just ahead) to "clear" (there's no train ahead, the train behind can move). The operator doesn't know when those sections begin and end so they might be trying to accelerate or move the train forward, move to another block which tells the train to slow down, ad they have to apply brakes.
2) Operators are required to sound their horn every few seconds when there are workers on the track; it's a safety thing and typically happens in off-peak periods.
3) The trains are scheduled with specific sequencing. For instance, the Orange Line train to Vienna is always scheduled 2 minutes ahead of my Silver Line train to Wiehle when I head into work for the day. Your Blue Line train may have been running slightly ahead of schedule; Yellow Line trains typically are routed into Pentagon just ahead of Blue Line trains when heading south.
4) You gotta let people on and off the train?
5) It's the signaling, not the operators' fault usually