In terms od the Air Launched Hawk, it's an interesting question. I've heard persistent rumors since about 1980. The thing is, it's not implausible. The Hawk seeker, particularly those of the early Hawks, is essentially the same as a CW Sparrow seeker. If you can figure out how to spool it up, separate it from the carrying airplane, and light the motor, it may very well work.
Some what if guns:
- The M4 gun designed for the USN's 28mm/1.1in round. Ballistics much closer to the .50 HMG, shell is heavy (~3 times heavier than on the Hispano 20mm), viable for firing an useful AP round (that needs to be produced). Yes, RoF will remain low.
- MG FFM scaled-up to 25mm; 200g M-shell @700 m/s. One for Bf 109s, two for Fw 190s, four for night fighters + schraege musik.
- A big MG 131, but for the 15mm shell of 57g instead of the 13mm one of 34g. Less powerful and lighter cartridge than the historical MG 151, doing ~750 m/s instead of 960, so the weapon can be lighter & more compact - talk around 25 kg? Hopefully ~850 rd/min. For self-defense as 'hand-held', for turrets, viable as AA weapon on vehicles. Also as a synchronized gun for the fighters. Copy the simple & cheap fuses from British and/or Japanese for this one.
- Soviets do the airborne gun that uses ammo from the 25mm AA gun - easier to install on existing fighters than the 37mm guns they had, far less recoil, still with devastating effect on aircraft of the day.