An AWACS is generally defenseless, relying on the fighters it helps control to protect it from attack. The actual radar horizon of the E-2 for example is highly classified but is at least 300nm and probably more. In the USN, the E-2 is data linked to the surface force and both share an integrated battle space picture. Every unit sees a combined picture generated from all the sensors in the strike group. Control of the fighters is coordinated with surface commanders. The defensive anti-air commander is not necessarily on the CV but more likely on a CG equipped with Aegis ( every CG now ). The E-2 does not act alone vectoring fighters to threats. There is a lot of computer power going on here as well to identify and prioritize threats. The same is true in the cockpit as most modern fire control radars will prioritize threats for the pilot or weapons officer to select.
Maximum altitude of most missiles depends on the altitude of the launch platform. Actual rocket burn lasts seconds, seldom longer. If a missile has to climb significantly or dive significantly this takes away from it's horizontal range. You have to think in three dimensions. Also a fighter on the deck can be given targeting data from a higher altitude asset with a longer radar horizon, or from a surface unit that is further out in the strike group. These aircraft seldome exceed 40,000 feet regardless of what the spec sheet says about their maximum altitude. What happens at high altitude is that your stall speed begins to approach your cruise speed, and the range of angle of attack the aircraft is capable of diminishes. Dogfighting at 40,000 feet is a lot more difficult due to basic aerodynamic limitations. Engine also do not tolerate high AoA at high speeds and altitudes.
Typically today a CV's escorts are well over the horizon from the CV due to the great range of modern weapons and sensors. It is nothing like WWII with the escorts grouped tightly around the "bird farm". This expands the strike group's radar horizon and increases the distance from the carrier that these ships may begin to engage incoming aircraft and missiles. If you thing about each ship having a hemisphere over it representing the range of it's weapons, you arrange these around the carrier so that they all overlap near the carrier providing long range air and ASW defenses. The Hummer sits above all of this.
Fighters will defend that AWACS. Lets face it, the Hummer is an aerodynamic slug. It has about a zero chance to protect itself. It would require a very long range missile system, and this implies you would need to devote space and weight to the necessary radars, fire control computers and install launch rails. This would greatly detract from the payload available for the Hummer's primary job of being an AWACS. Mounting something like a Sidewinder would be futile, there is no possilbe way a Hummer could maneuver sufficiently to get a shot off. For AIM-9X for example to make anything but a frontal shot ( implying the Hummer was lined up on the fighter, ha, good luck ! ) you need helmet mounted sights with all the ancillary stuff in the cockpit to track the pilot's head movements. The limited visibility from a Hummer's cockpit makes this a fantasy. You would need to have a bubble canopy and still the rotodome and those two big engines would limit where such a pilot could see. For many types of engagements even older 'Winders require the seeker to be slaved to the aircraft's intercept radar to achieve lock. No IR or IIR sensor can detect anything much beyond ten miles. This is a basic limitation of all such seekers. If something hostile makes it within ten miles of the Hummer the crew might as well bail before they are blown up cuz it will be over in a few seconds. It is pure fantasy for a Hummer to launch missiles to defend itself. Nope, the Hummer or any AWACS is completely reliant on other fighters for it's self defense, or from the missiles of the surface units in the strike group.