Can you still go and see the outside of the lighthouse after hours?

You can certainly see it, but the gate to the actual Lighthouse compound is locked and the State Park closes at dusk. If you're interested in seeing it at night, MAC offers Full Moon Lighthouse Climbs. It's an opportunity to climb at night and the view of the surrounding area and the water is spectacular! Check their web site for dates and times.

Yes

Yes you can

Yes. It is gated on the outside but large enough you can see it from a distance.