Beach House with only a Fridge and Microwave

If you're driving, buy a small portable table top grill. (propane or charcoal)

I love to steam fish in the microwave. I season with a little salt and Herbes de Provence, place in a glass (pyrex dish), cover (usually with saran wrap) and nuke for about 4 minutes for a 1 lb filet. Fast, easy, no prep.

Okay..scratch the 'sausage' element for the 'low country' shrimp boil suggestion...

Add crabs..or more shrimp.

You really need to look into portable 'hot plates' for cooking if you only have microwave.
Is there a grill at the rental?

Consider getting an electric burner or a camp burner. Electric would be safer.

Heat up a big pot...put in a can of beer..and an a lemon cut in half.
Add a bag of Zatarains 'crab boil'. (the dry stuff in the bag)..and simmer that to get the flavor out. (the beer helps extract flavor from the dry spices in the initial heating step).

Okay...fill up the pot with water and some salt. Let that come to a boil/simmer.

While you cut up...red potatoes. Add those now...they take longest to cook
Summer Sausage....in disks and dump that in.
Wait...let all that cook about 20-30 mins.
Then add corn on the cob shucked and cup up in thirds.---just BECAUSE.
After the potatoes are tender...and susages float...
Add about 2 lbs of shrimp with the peel on...and another lemon cut in half and juice.
Then turn the heat off and wait about 15 mins until the shrimp are just right. (you're eating and testing this all the time).

Okay.....if it all seems done...Dump it all out on news paper on a picnic table with butter for the poatoes and corn...and cocktail sauce for the shrimp.
Side salad and bread.

Equipment:
Big Stock Pot....with the strainer insert.
A table top burner grill thing 'hotplate' that will boil water for the stock pot.
News paper.
Cutting Board...and napkins.

That would be more a night dinner thing....
For lunch..salad, sandwiches..cold cuts..snack plate. Serve yourself thing. And fruit.
Watermelon...cut up fruit salad..etc. Lettuce wraps with veggie fillings.

I made quinoa (gluten free) with greek accent for dinner last night. Tomato, cukes, scallion, black olives and vinaigrette. Did some Feta on it also. Served it with lamb chops and roasted asparagus. Came out great! You could do something like that and sub out a fish for the protein.

Rice noodles are a great gluten free option. They just need soaking in boilling water, and tossing with a nice microwaved sauce, (maybe a Pad Thai something?). This recipe sounds delicious: https://food52.com/recipes/30969-vegan-pad-thai

I like to cook spaghetti squash in the microwave. It takes a while, but it comes out perfectly. Throw some pre-made pesto on it and you've got a light and easy meal perfect for beach weather.

These are all great ideas! Thank you so much. I think a buffet set up that incorporates these suggestions will be perfect for lunch and dinner.

I realize that this doesn't address the specific needs of your crowd, but I'll include it anyway for others reading this thread who are interested, and not subject to your restrictions:
For years, my mother made enormous quantities (serve 14 for dinner, plus leftovers for lunch) of pulled pork, which she'd freeze and then take, frozen, to the beach. Defrost in the fridge, heat in the microwave, along with the buns. Make cole slaw, serve, enjoy! Recipes for both (my Cuban adobo pulled pork, and a fairly basic slaw) are here: https://food52.com/recipes/4872-cuban-adobo-pulled-pork-and-slaw-sandwiches

Buy sandwich rolls or hamburger buns, or, if you like to bake bread, try this recipe. I've recently perfectly my sandwich rolls, inspired by the classic enriched rolls found everywhere in Tampa, where they're used for Cubans: https://food52.com/recipes/36304-cuban-bread (If you don't want to use shortening or lard, use olive oil or soft butter.) ;o)

Do you know if you have an outdoor grill available?

How about salad nicoise for dinner? It's elegant but not fussy, devoid of gluten and red meat, easy to transport because everything stays pretty solid, can be made in quantity, actually designed to be prepared ahead of time, and you can assemble it right before eating. (It's nice to serve with bread, but given it already has the potatoes I hope the gluten-free person won't feel deprived.) I'd also suggest gazpacho, can be served with tortilla chips, and I love the ceviche suggestion. Any kind of salad (or gluten-less grain salad) would work.

Thought of something else! Ceviche might be nice with a big salad and some fresh fruit for one of the meals... Plus, there's plenty of GF tortilla chips out there you could serve on the side for scooping.

A caprese salad could be a nice no-cook starter for your lunch.

sounds like it's hard to make a single main dish that will satisfy all your guests. perhaps a buffet approach offers a way to make a festive meal all can enjoy [say, with a single starch (e.g. sweet potato) edible by your GF friend and a choice of mains, or a single main (e.g. fish) and a choice of starches]

If you'll be driving, you might consider doing a little easy prep at home and bringing some items with you - cook a big pot of grains, for example, or bake a couple loaves of bread that can be cubed for panzenella or sliced & toasted for bruschetta.

This cabbage peanut salad is perfect summer party food, and pretty filling on its own:
http://lookimadethat.com/2011/05/27/cabbagepeanutsalad/
You could chop all the vegetables and prepare the sauce in advance, and toss them together shortly before eating. The salad keep pretty well once dressed, but the texture is best in the first hour or two. I often top it with (or toss in) salt-and-peppered wok-fried tofu to make it a standalone meal. You could do the same with some tofu/meat/seafood already prepared by a deli.

I love making zucchini noodles (top with pesto or tomato sauce or a sesame-peanut sauce) -- good for any kind of dietary need and really delicious if done right. Once prepped, you can serve them raw, quickly cook them in boiling water, or zap them in the microwave for a minute or two. For something heartier, add shrimp! Here's a link: https://food52.com/blog/10742-3-ways-to-make-zucchini-pasta