A friend asked for two easy hot hors d'ouevres and one cold one, easy and tasty!

Cheese platters all the way with some dried fruits and nuts and a veggie platter with hummus. Bruschettas are also great. And I should suggest these interesting dates https://food52.com/recipes/33892-renee-erickson-s-sauteed-dates

For cold - I love ham and pickle wraps. Take room temp cream cheese, spread on a slice of deli ham, place whole pickle (not spear) on one side, roll up around the pickle. I prefer to refrigerate for a few hours at this point, it's easier to cut and stays together better. Stick toothpicks in every inch or so and cut between them to make bite-sized pieces.

gosh, given all the possibilities, it would be helpful to know the country! my advice for someone in coastal CA would be very different from my advice for England. and when is this for?

I agree with Windischgirl, raw veggies are a great idea, even as simple as just carrot sticks and hummus. Another good idea are slices of cheese. You can either go for the pre-sliced selection, or buy a block and cut into small wedges. Serve with either nuts, cornichons, crackers, or all of the above.
An easy hot option is pizza bagel bites. Slice mini bagels in half, spoon on tomato sauce, and top with shredded mozzarella. Broil in oven for 5-10 minutes, or until cheese is melted.
For a bit of a fancier bite: clean and remove tails of jumbo shrimp, slice in half, marinade (or just toss) in pesto, then pan-sear. Skewer with a toothpick and serve.

For hot:
sauteed chicken livers on toast (all you need is frypan and toaster or grill)
artichoke crostini (see Mario Batali easy recipe at smittenkitchen.com)
For cold, an old James Beard classic:
Sweet onion (Vidalia or whatever varietal you can find) sliced thin, on mini brioche with mayonnaise. (simple but good)

Thank you, everyone!

This combines hot and cold, bagna cauda https://food52.com/recipes/8936-bagna-cauda-al-la-vecchia

For a hot one, how about mushrooms stuffed with cheese and pesto or sausage?

For the cold one: an absolute staple at my every gathering is a tray of assorted raw veggies. It's fresh, light, and easy to eat...they disappear like chips! Make it colorful and bite-sized. Dip--like hummus--is optional, but often appreciated. Another quick one is a package of low fat cream cheese (Neufchâtel) placed in the center of a dinner plate and topped with a high-quality jarred salsa (it's cooked so it's runnier, which is what you want) OR cocktail sauce OR a runny cranberry sauce. Use wheat crackers to dip into the sauce-cheese mixture. Hot ideas: place a sheet of puff pastry on a cookie sheet and score a 1/2 inch rim. Top with shredded Gruyere then asparagus spears, black pepper and any dry herb. Bake this till brown.