Hello Juan!
Sorry for the late reply.
Aircraft range in distance or endurance in time will vary widely depending on three main parameters...configuration, altitude,and speed.
Configuration has to do with total fuel on board as well as total drag. External tanks and weapons have a significant drag penalty that cuts into both range and endurance.
Altitude is a major consideration. Jet engines are much more efficient at high altitude...sometimes high altitude range can easily be twice the low altitude range or more.
Lastly, speed is important in that high speeds mean high fuel burn rates which tends to mean shorter ranges, less endurance.
The F-4 can carry three external fuel tanks. If the mission goal was to just fly from one point to another, then the F-4 could go at least a thousand miles. But this is misleading since it means a high altitude cruise with no weapons on board and no consideration of enemy attack.
If we consider a typical F-4 configuration of two external fuel tanks, missiles, and six bombs, then a range of about 400-500 miles might be more realistic. This would give a combat radius of about 200-250 nm maximum.
Missiles can certainly fail once "locked". The reasons include mechanical failure, electrical failure, loss of target signal, inadequate range, inability to match target maneuvers, etc.
The most common defenses against a missile are chaff, flares, and other electronic counter-measures such as jamming, spoofing, range gate stealers, etc.
Today, it is possible to use guidance methods that do not require the attacking aircraft (or pilot) to "see" the target. The most common of these is inertial guidance...the fighter missile computer gives the missile directions to fly to a particular point without any need for the missile to use radar or IR target tracking. Once the missile flies to that point, it will have to use radar or IR to acquire and track the target.
Andy