Let’s get creative. I’ll give you two ingredients that aren’t typically used together. You come up with a dish that incorporates both of them. You may add other ingredients, but the two challenge items must figure prominenently in the final item. Then you pick two new ingredients. The only rule is that the ingredients must be actual food that is consumed. No chewing gum, toothpaste, or other non-food items. Let’s begin. You have a bag of frozen, raw shrimp (peeled and de-veined) and a box of Velveeta.
Shrimp mac & cheese. Beef short ribs and vanilla instant pudding.
Asian short ribs. Braise for forever and make a sauce out of the vanilla pudding, rice wine, ginger, lemongrass, fish sauce, etc. Thin and umami-rich.
Ahi tuna and cotton candy.
Caramelized tuna.
Duck and anchovies
Roast the duck. Use the collected fat to make a sauce with the anchovies…maybe some lemon and a few capers.
Fresh clams and iceberg lettuce.
Clam ceviche served one-bite salad style on an iceberg lettuce leaf.
Chicken thighs and marshmallows.
Skin and grill the chicken thighs. Melt the marshmallows in a double boiler and season with berbere to make a hot/sweet glaze. Would need to apply it carefully to avoid burning the glaze.
Portabella mushrooms and cocoa powder.
Chocolate cream of mushroom soup.
Peanuts and eggs.
I’d probably do some kind of curry. Hard boil the eggs, cut into pieces, and make a spicy sauce, like an Indonesian egg curry. Probably add whole the peanuts in with the sauce and simmer till they’re starting to get soft. Alternatively, I might make an egg curry with a peanut sauce similar to a Thai peanut sauce.
Next: Chickpeas and ground coffee
I had the same thoughts on the egg and peanut.
I’d do some kind of chickpea dessert. Chickpea brownies with coffee aquafaba (whipped cream substitute made from chickpea liquid.) Something in that direction. Or, for savory, you can go chickpea chili with coffee in the chili powder mix.
Pork cheeks and rhubarb.
Brown pork cheek chunks then simmer in pineapple juice for an hour or two, added chopped rhubarb, continue to simmer adding water as necessary. Add pineapple chunks and heat throughly, reducing sauce. Stir in chopped cilantro and serve over pasta shells. You can add some shrimp to round it all out.
Lobster tomalley and bananas
I’m going to assume the bananas are green, as they usually are in the stores here. I’d cut up the bananas and deep fry them to make french fried banana. I’d saute onion and or/garlic in butter along with the tomalley and some parsley. Then use a hand blender to give it a smooth texture. Serve the not banana fries with a little salt and the tomalley mixture on the side as a dipping sauce.
Baby eggplants and a bag of smoked almonds.
Eggplant? The OP specified “no non-food items.” 
Since frying is the only way to make eggplant even remotely edible, I’d see if I could grind the almonds and mix with some regular flour to use as a dredge for smoky eggplant fries.
Serrano peppers and bosc pears.
[Moderating]
Moving from CS to Thread Games
Spicy pear marmalade.
Peas and flounder fillet.
Broiled flounder topped with baby peas in bechamel.
Canned corned beef and popcorn.
Assuming you mean plain popped popcorn, with no additions or seasoning…
Use the popcorn to make a savory cake or cracker, similar to a homemade rice cake (like this). Essentially you coarsely grind up the popcorn with a binder like eggs and flour, then bake until crisp. I’d probably bake in a single thin sheet, then break the results up into irregular crackers.
Use the canned corned beef to make a spread of some kind. Maybe mix it with some good quality coarse mustard (which makes almost anything palatable), finely chopped onion, etc.
Serve as hors d’oeuvres.
(Full disclosure: I’m a vegetarian and I haven’t had corned beef in eons. I miss good corned beef. I’m not sure I’d be tempted by canned corned beef though. That looks awful.)
(Aside: pulykamell, I like your chickpea dessert idea! Aquafaba is pretty interesting stuff. My wife has been experimenting with it. She made some excellent cookies with it a while back.)
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Next: cocktail onions and old fashioned rolled oats**
Hors d’oeuvres again.
Drain the onions and let dry a bit. Mix oats with just enough butter and flour to hold together, wrap each onion in a thin layer of oat mixture, and bake briefly on a rack in a hot oven, just until crisp.
(Aside: TriPolar’s marmalade sounds good, but my first thought was to poach the pears in white wine, fill with ice cream, sprinkle with toasted nuts, and drizzle on a pepper syrup. Second thought, I might do the marmalade instead.)
Next: Salami and apples.
Peel, core, and cut the apples into 8ths. Wrap each piece of apple in a paper-thin slice of salami. Drizzle with balsamic vinegar.
Fresh stringbeans and frozen strawberries.