Q1 and Q4, Yes the loose black/white wire needs to attach to the black wire on the other white connector. You also need to extend this wire and attach it to an earth on the car.
Q2, The loose blue/white wire thats with the black one needs to connect to the amp remote wire from your new headunit, its normally a blue wire coming our the headunit harness.
Q3, And yes you need to connect the steering wheel remote wire to the JVC patch lead that you brought.