D307 is notamned permanantly active up to 5000ft, and is notamned to higher levels at other specific times, these are widely published on the charts and by AIS, and also available from London FIS.
Live firing only takes place within the confines of the Danger Area, this could be on the ground, air to ground, air to air, or a combination of all, at any time.
The AIAA is exactly what it says, military aircraft operating in the AIAA and into and out of the Danger Area are for the most part subject to the rules of the air, but sometimes the nature of their exercise makes this impossible to comply with - again this sort of activity is notamned on a daily basis.
Although the AIAA is in the open FIR, it is for the most part over the North Sea, and there's no real problem if you do want to fly through it, as long as you take advantage of a radar service and fly at a reasonable altitude (above 5000ft would be sensible).