Not so sure about that, as the F-15 has sufficient visibility over the nose for navy purposes and it's nose is big enough to accomodate an AWG-9 radar (assuming it was mounted further back in the nose, closer to where the cockpit is -- me and another member on WHIF had discussed this and concluded this)
Not according to the Navy, without modifying nose and/or elevating pilot's line of sight for constant angle of attack for carrier approach technique
I don't believe the F-15 carried a 36 inch flat plate antenna, and it's the antenna that is really at issue here, since it has to be able to move around. Whether you could fit the entire AWG-9 into an F-15A is not germane, since the F-15, and its nose, was not designed to do so, so why would they build such a nose? As far as moving it back, what happens to all the stuff that's already behind the F-15A's APG-63?
Now they probably could have built a carrier capable F-15, and they probably could have put the AWG-9 in that, but then, the front of the a/c would no longer be the Eagle snout that we know.