1: What is the purpose of the BLUE circle, what impact does it have? Does it mean the fleet will return to homebase as long as it is inside the blue circle?
Each blue circle marks the area of operations of a fleet in defensive posture. The area of operations is centered upon the home base of that fleet. A fleet in defensive posture will, at least in theory, respond to attacks made on things belonging to your empire within its area of operations. A fleet in defensive posture will not normally leave its area of operations except to refuel (if the nearest location with enough fuel for the fleet is outside the area of operations); if the area of operations is small enough (<= system) or the fleet is very close to the edge of the area of operations, portions of the fleet may leave the area of operations when attempting to escape destruction at the hands of an overpowering opponent, if the ships are permitted by design engagement stances to flee. The area of operations will become undefined if the home base is lost or destroyed, at which point the fleet will behave as an automated fleet with no home base or area of operations set.
2: When would somebody ever use defensive posture? What is the idea behind it?
3: How do I set up a fleet to f... up enemies that comes into my domain. I need an enemy base to use "set target" - So I can only get the RED circle centered inside enemy territory.
The idea behind defensive posture is the the idea embodied in the first part of your third question. A fleet in defensive posture will, in theory, attack any hostile targets which attack your empire within the fleet's area of operations. Note, however, that defensive posture is largely reactionary.
Because fleets in defensive posture are largely reactive rather than proactive, defensive postures tend to work better when the things being protected are nearby, reasonably tough relative to the strength of the attacker, or both. If you intend to use the "nearby systems" (anything within a radius of 0.25 sectors of the home base), "sector" (anything within a radius of 0.5 sectors of the home base), or "anywhere" (anything belonging to your empire anywhere in the galaxy) settings for the area of operations, you need to ensure that the targets can hold off an attacking force long enough for your defense fleet to arrive. Especially early in the game, this essentially rules out areas of operations larger than "nearby systems" if you plan to use only a single fleet to cover the region, except perhaps if that region is under very little threat; at normal game speed, ships equipped with fully-upgraded Gerax Hyperdrives or the initial versions of the Kaldos Hyperdrive, Equinox Jumpdrive, and Calista-Dal Warp Drive take at least 40 seconds (including jump initiation time) to reach a location 0.25 sectors away, and all earlier hyperdrives take longer. Any attacker which is a credible threat to a target can do a lot of damage in 40 seconds; 40 seconds at normal game speed is probably enough time for an average size-300 warship to cripple or destroy a standard-template mining station or for a decent fleet to seriously damage a medium space port. At 0.5 sectors' distance (maximum distance from the center of the area of operations using the sector setting), ships equipped with the initial versions of the three midgame hyperdrives or fully-upgraded Gerax Hyperdrives will take over a minute at normal game speed to arrive and will probably arrive too late to stop a serious attack on anything short of a heavily-fortified colony. You can use local defense fleets or invest more heavily in station defenses to buy more time for fleets with large areas of operations to arrive, and you can use multiple fleets with overlapping areas of operations to make it more likely for a defensive fleet to be available to respond to attacks; regardless, I would not recommend ever using the "anywhere" setting, and I would not recommend using the "sector" setting for defensive-postured fleets equipped with any hyperdrive much slower than the first upgrade of the Equinox Jumpdrive.
< Message edited by Aeson -- 3/22/2016 12:12:45 AM >