I don't really understand what you are trying to do with the synchronisation, "Multiplayer re-synching so the strobes start at the same time each time a cycle is finished.", which presumably uses lightsynch.sqf, so I can't say whether it is working as you intended.
What lightsynch.sqf does is regulate the time when strobes begin again after they have reached the end of the runway, it is also used during single player operation. It is like a metronome. The clients that are ready (the ones that have finished their last strobe) wait for the value to be true before they start the strobes again, they will all start at the same time give or take a few milliseconds. So basically what happens is this: different peoples framerates cause them to have slight differences in the speed of the lights movement, but no matter how out of whack they get from one client to another, they always wait for the server to tell them when to start again. I chose this rather than than true multiplayer synching because I don't want someone with a low framerate messing up the effect for everyone else.
3) When you turn on the strobes, you turn on the strobes at the closest airport, which is correct. When you turn off the strobes, you turn off the strobes at the closest airport, even if that airport isn't the same one that you turned strobes on at beforehand. At least as far as I can tell...
The switching script I wrote does exactly as you say. But there is more than one way to skin a cat!

The lights can be activated/deactivated however you wish. For example, place a trigger over the airfield and use:
lightswitchonoff set [airportidnumberhere, true];
for the act
lightswitchonoff set [airportidnumberhere, false];
for the deact
The array lightswitchonoff holds the values that switch the airports off and on. Use triggers, write a small script, whatever. The sky is the limit on how you want to change those values!

Of course I do plan on including more activation scripts for different situations but no point in doing so until I get things down a bit tighter.
As an aside, clients will only check the switch status of one (the closest) airfield at any given time. If someone say leaves the lights on at pita for some reason, it won't be eating up the resources of people who are closer to antigua.
I have a good idea of some of the other things that you might find strange, hit me up on msn for those. I also have some questions for you.