Some comments, in no particular order:
For AI use, it does not matter if a group is marked autofire or not. It matters a great deal what weapons are in which groups, however - I've had cases where the AI simply refused to fire certain weapons, and re-adjusting weapon groups fixed that. Generally, this is easy to test using the simulator from the ship refit screen - go in, put up some opponents, and put your ship on autopilot (default key is 'u', I think?).
LR PD Lasers are generally a bad choice - there are some situations where they work well, but most of the time you're better off with tactical lasers... which aren't PD at all. For the Hammerhead, I'd suggest replacing the LR PD lasers with tactical lasers... and the PD lasers with Burst PD lasers; it'll give you better overall protection from missiles, and the tactical lasers are decent anti-fighter & support weapons.
Then again, I always prefer a primary setup of kinetic guns; a pair of heavy needlers would do nicely, or one heavy needler and one heavy mauler. Assault Chainguns are usually not that good; low per-shot damage means they aren't awesome against armor despite being high-explosive type. My suggestion for a hammerhead loadout would be:
1 heavy mauler, group 1, manual control
1 heavy needler, group 2, autofire defaults to on - with the note that you'll turn autofire *off* during combat if you're getting high on flux, facing an overloaded or otherwise unshielded target, etc.
2 tactical lasers, front turrets, group 3, autofire - you'll only turn this off if you're up against something with decent shields, in which case they're not worth the flux to keep them online. Usually I'll just leave them on.
2 burst pd lasers, back turrets, group 4, autofire - leave this online basically all the time.
- and, yes, nothing in the small missile slots; I'd rather spend those ordnance points on vents, capacitors, and hull mods. Your mileage may vary, but I tend to find the heavy mauler is strong enough that you don't really need missiles.
Eagle: As with hammerhead, you probably want to upgrade to heavy maulers & heavy needlers when you can (limits including cash, available guns, available ordnance points). Mining blaster probably best dropped - very flux inefficient, and the eagle doesn't have that much to spare, plus the antimatter blasters & heavy mauler both nicely cover the high-per-shot-damage armor-cracker niche. I'd suggest graviton beams for the three medium turrets - they're highly efficient, good anti-fighter weapons, and generally pretty effective at putting pressure on shielded targets; with those installed, it might even be worth considering switching main guns to 2x heavy mauler, 1x heavy needler. And, last, burst PD - at least for the rear two turrets that are covering your engines.
Edit: Oops, forgot one important detail. The eagle is a cruiser. You just about always want either Dedicated Targeting Core or Integrated Targeting Unit on a cruiser or capital ship; they really make a big difference.
Enforcer: I don't use enforcers, so someone else will have to offer advice here. Only thing I will say is: flak cannons are awesome point defense weapons; dual flak even more so (though regular flak is cheaper and usually plenty) - I'd consider replacing the light dual machine guns with flak cannons.
Medusa: An excellent ship; especially survivable if you can add extended & accelerated shields. For anti-pirate work, I'd suggest a primarily beam setup - gravitons, tactical lasers, maybe a burst PD or two (I usually go with either the two rear side turrets, or the central rear turret & the two front small turrets). Perhaps add some small kinetic weapon in the front hardpoints - railguns, maybe?
Alternately, fit it for a strike role - heavy blasters, some PD or tactical lasers, and as many vents & capacitors as you can cram in. Unstable Injector might also be a good call - let it get in & out of strike range a bit more easily. Play around with the simulator some, see what actually works; heavy blasters are exceptionally flux-hungry, and letting the AI use them could just be a recipe for a dead Medusa.
Apogee: The Apogee is at its best as a flagship - under AI control it will frequently set its drones to roaming, letting them wander out of its shield bubble where they're much more likely to die. Still, even under AI control, it can do pretty well; just, in that case, you may want to favor more flux-friendly loadouts than heavy blasters or plasma cannon. For Apogee loadouts, I suggest looking here:
http://fractalsoftworks.com/forum/index.php?topic=5446.0 - in particular, the first one in
my post might be a decent template to work from.