Regards,

If this is the case, I recommend timing how long it takes to make about 1/4 revolution, set exposure for that, adjust lens aperture and use a different film speed if necessary if you cannot open up the aperture sufficiently for the exposure time. Then time your exposure so that it spans the quarter revolution just as the beam becomes visible from the far side of the lighthouse (presuming there's one beam and not two back-to-back).

This will likely require some experimentation.

A couple of questions:
There are a number of different "Mamiya 645" cameras around:
(a) original M645, M645j and M645-1000S
(b) M645 Super
(c) 645E
(d) 645 Pro TL
(e) 645AF
Which one do you have?

I have the original M645 and it cannot control flash output. With a "waist level" finder the X-Sync PC socket on the left side near the top rear of the body is used, and a cable is run from it to the flash. The M645 prism finders have a hot shoe on top with a single center contact for triggering a flash if its mounted there (also can be used instead of the X-Sync PC socket to run a hot shoe adapter and cable to the flash). With an M645 you have two options for flash usage (using either the PC socket or a prism finder hot shoe):
(1) An "auto" flash must be able to control itself using its own built-in sensor. This is what I usually do with a number of flash heads.
(2) The alternative is running the flash in "manual" mode and using its guide number and subject distance to set the lens aperture.

If the 5200 can be triggered using a cord (this allows mounting it on a flash bracket), there should be a small socket (round hole) on the side of your flash that takes a miniature phone plug on one end of a flash trigger cord. The other end of the trigger cord would have a PC plug to fit the PC socket on the camera body. I use a flash bracket with the M645, mount the flash head(s) on the bracket, and run a trigger cable to the camera.

If your 5200 has more than a single center contact on its hot shoe, I don't recommend mounting it in a prism finder hot shoe. The M645 prism finder hot shoe is likely to short out other contacts as it is all metal except for a small ring around the center contact. You can also end up the additional contacts hanging up on the outer metal ring around the contact making it difficult to remove the flash (been there, done that, and had to disassemble the prism hot shoe).

(1) prime lenses are less susceptible than zooms,
(2) Use a lens hood and/or shade the lens with hand, hat, etc.,
(3) Remove superfluous filters, use high quality multicoated filters,
(4) Smaller apertures may increase flare, do DOF preview to check for flare,
(5) Make sure the lens is clean (no streaks, no dust particles),
(6) Flare should be apparent in your viewfinder. You can often change position or point of focus slightly and eliminate the flare.

More info at:

http://jonathanclark.com/diary/flare/

Although there are other possible causes, this particular effect is a classic example of reflections from filter surfaces (front and back). It's possible for this to occur even with multi-coated filters, although it reduces the prominence of the "ghosting." If you were using a filter, take it off and try it again; I'd bet dollars to donuts the "ghosting" goes away.

Re: flourescent lighting (more likely mercury vapor in basketball court) Fuji Superia X-tra 400, and 800 have 4th color layer that helps.

If you don't use the flash, an FL-D filter will correct typical flourescent light to daylight film. Don't use this filter with the flash as your near subjects will be too pink.

Jon's made a good film recommendation, but I disagree with using an FL-D filter for color correction. For all that's gained with a faster lens, it all goes away with an FL-D, including making the viewfinder much dimmer. The FL-D is not a pale filter; it consumes one stop of exposure. These types of decisions are always a trade-off; I'd rather have the brighter viewfinder and faster shutter speed(s). Most gymnasia use mercury or sodium vapor lights, which are neither tungsten nor fluorescent. Filters for color correcting tungsten or fluorescent to daylight film will not correct mercury or sodium lighting to daylight.

See my tutorial about doing just what you've asked about:
http://johnlind.tripod.com/wedding/

With the time you have prior to the event, make use of what you can and tailor what's there to your specific situation. This is a very, very basic "survival" primer. The complete subject of wedding photography for those who do it for a living is enough to fill books (emphasis on plural: books).

Most important, enjoy yourself while doing it. It is hard work, and a long day, but can be fun if you allow it to be.

More seriously:
Without actually seeing exactly what you are trying to do, and where you are doing it, here are a few suggestions based on what I've seen others do:

1. If your area tends to have clear nights and the moonlight illuminates them, then get a chart of the moon phases along with moon rise and set times and time your outings to make use of a 3/4 to full moon at a time when it will illuminate them. The moon follows about almost the same path as the sun. You can judge what the moon will illuminate, and when, at a given time of year by watching what the sun does during the day.

2. Some will use a remote flash with radio or infrared slave and set it up near where the subject(s) are located. An umbrella or soft box reduces flash harshness. Work with flash angle to control shadows and get the lighting you want; it doesn't need to be (and probably shouldn't be) from the camera direction. A variation of this method opens the camera shutter using the "B" shutter speed, triggers the flash using a cord to the remote hot shoe it's mounted in, then closes the shutter again. If the flash has an auto sensor, it should generally illuminate the subject properly regardless of where you are. With this method you get one shot at it for some time as the flash usually startles the subject considerably. You may have to experiment with flash location (distance), lighting angles and possibly how much diffusion you are using on it. Use of artificial lighting is almost always obvious in these photographs also.

Couldn't resist the tripod remark, I presume with a mirror lens you're already using one.

Completely sealing the camera in a plastic bag is unnecessary if you have a "never-ready" case and/or a camera bag with top that closes up. I case the camera in the bag before puting it in the car or taking it indoors when doing very cold weather work.

Another issue you may encounter:
If your camera has an electronic shutter, it may suffer mirror "lock-up" or complete failure to function. Battery voltages drop under severe cold conditions and they can fall below what's necessary to operate the camera electronics. Warming them brings the camera "back to life." LCD panels on current SLR's and digitals may also cease to function in severe cold. If this occurs, most users will keep the camera warm under their coat until it is used and then return it there to keep it warm. Others will keep a spare set of batteries in a pocket to keep them warm and switch them. The alternative is a completely mechanical camera. Temperatures at which these effects occur, and how long the camera must be exposed to them vary by camera make and model. Usually it must be below about +20F.