You mean the 2x4 plastic panels you find in office lighting environments? I would think "no way!" can these be used. They're not very strong, brittle even (depends on what type of course) but to my knowledge also they wouldn't hold-up under direct sunlight; they'd likely discolor or worse, self-destruct.

Depending on how far down you are dropping the ceiling. If it is 3" mount a 54151LB light box to the floor/ceiling joist and add 2 box extensions to be even with your drop ceiling. Or you can nail a 2x4 lenghth wise to your floor/ceiling joist to the distance of your drop ceiling and put the light box on the 2x4.

You could really have fun with this! How high is the ceiling? Are you looking for a flush mount or pendant? If a pendant would work, perhaps something like this one from Rejuvenation would work. It's rather expensive, but something similar could be found. Or maybe a lantern of some kind, glass or pierced tin. If you need flush-mounted, Ballard's has a Moravian star that would be a nod to the nautical, but less predictable than the usual. http://www.ballarddesigns.com/moravian-star-ceiling-mount-mercury-glass/lighting/ceiling-lights/245459?defattrib=&defattribvalue=&listIndex=13 Or this one: http://www.ballarddesigns.com/star-ceiling-mount/lighting/ceiling-lights/210668?defattrib=&defattribvalue=&listIndex=10 Here is a link that might be useful: Rejuvenation pendant

I'm agreeing with Linda--paint the grid to match the tiles and hope that the ceiling just sort of disappears. Or you could investigate if there are any other tiles that could be substituted in place of the ones you have now. If paint is too heavy, I'm not sure that there's much that will be lighter. If you found really, really thin plastic, my guess would be that the thinner the plastic, the more difficult it would be to get it completely smooth. A wrinkly ceiling would bother me a lot more than a standard one with the holes.