Not neccessarily. There is no reason to take off with full tanks if you're just scrambling to intercept incoming bandits in your area. It's more logical that RAF fighters would have launched with partially full tanks to reduce weight and increase climb rate and combat performance.
Not likely. Since they didn't have AWACS in the era, analysis of what the radar suggests is largely based on only heading, altitude, and speed of the target object. It is true, that some sorts of data are better provided by radar operators than the 'dot dar', but still, they didn't get real-time updates.
This would mean planes would have to search the directed areas. There could be decoys and clever ploys to fool radar, and once it became clear, planes would have to redirect themselves immediately to the next point - something, which is impossible if they are fueld up for only one search&destroy engagement in a local area.
The defenders are usually the 'waiters'. Passive local defense as seen in the BoB require planes to be ready in the air, and relocate themselves according to the attacker's moves. Thus, in a sense, the attacking side with precise mission directives would have exact requirements on the amount of fuel needed(which was still too short, in the case of the Bf109s), but the defenders would never know whether or not a certain amount of fuel would be sufficient or not - thus, it is likely that carrying maximum amount of fuel available was mandatory.
Even in AH, only small limited engagements and low-alt furballs are likely to be fought with something like 50% fuel. For instance, in a furball near a CV, I'd take a F6F-5 or a Seafire with just about 50% fuel.
However, if one looks in a wider aspect, and prepares to defend the CV by means of CAP, then I would take the F4U-1 with larger internal fuel load with 100%, since I never know exactly when the enemy would show up.
