Falcon #1833 - Your questions have been mostly answered by others but, yes, Police Pilots are used to launching for a job, and being re-tasked in flight to somewhere else, at any stage in the flight. One does not generally brief for a flight, you brief for the whole shift, since you never know what/where you're going to go to - an update brief will normally just relate to an unexpected pax or extra fuel (endurance) required, or possibly a longer range unusual task, most likely to be slow-time & planned, rather than immediate/reactionary. Almost every flight is a constant re-prioritising exercise juggling tasks, distance, weather, fuel, alternate base/fuel, etc.
As has also been intimated by others, whilst you can reduce fuel consumption (e.g. sitting in the hover into a 20-30kt wind for 20 mins) that period seldom lasts long enough to make more than 5 mins difference to a typical 1:45 - 2:00 (night) endurance, since the rest of the time you're normally rattling along at Max Cont to get to/from jobs as quickly as possible - it generally works out at a very steady 200kg/hr for airborne or ground calculation purposes.
Rustchaser - skadi is correct, and if you read the thread in full, you'll see that rotor brake theories have been discounted by numerous posts early on. In any event, the 135 rotor brake requires a very conscious decision to pull an overhead lever out of its stowed position and apply it (FLM says below 50%). You'll find most pilots are uncomfortable enough about pulling it on at 50%, & leaving it to stop, as part of the rotor brake proving process when the pads or disc are changed!