Do we need to replace wet insulation resulting from a a/c drain
You don't have to replace insulation unless you think that you can't dry it.  Normally we would set up halogen lamps and fans to dry attics out.  You can replace it too if that seems easier.  How do you tell?  Well after 1.5-2 days of lights and fans things should be bone dry.  If not you probably need to replace.  For instance in the winter we know we can't get enough heat and air going so we would just replace.

As for your ceiling, drywall can get wet and if it fully dries it retains 90%+ of its structural abilities.  There was actually a study done I read about wetting and drying ceiling drywall 50+ times and basically they found if it dried right after it got wet you could basically get the drywall wet an unlimited amount of times.  However if it is wet too long then the gypsum starts to break down.  How do you tell?  You will probably see all of you screws/nails popped out down.  

If you just have a couple that popped out I would wait for it to dry then add screws back where needed.  You might have to do some very minor mudding/sanding.  If you don't want to do it pretty much any handyman/contractor/dry wall service can handle this - about the easiest job you can get.

If the drywall is just too wet to salvage, you simply need to remove all insulation on top of it, take it down and redrywall - and then put back insulation.  This isn't hard but is a mess.

To get rid of the stains you need an oil based stain cover like the original Killz.  If you try anything else you could end up putting 20 coats on.  Usually 2 coats of Killz and then two coats of ceiling paint takes care of it - you can double coat within an hour for each with correct air flow.

As for your light - I would assume it is fine if it is dry and still working.  I would not be concerned about that.