The last time I was at the frutería, I bought some fruit I didn´t know anything about.
The green lumpy things are Cherimoyas, or custard apples.
The fruit is oval, often slightly oblate, 10–20 cm long and 7–10 cm diameter, with a smooth or slightly tuberculated skin. The fruit flesh is white and creamy, and has numerous dark brown seeds embedded in it. Mark Twain called the cherimoya "the most delicious fruit known to men." The fruit is fleshy and soft, sweet, white in color, with a sherbet-like texture, which gives it its secondary name, custard apple.
Some characterize the flavor as a blend of banana, pineapple, papaya, peach, and strawberry. Others describe it as tasting like commercial bubblegum. Similar in size to a grapefruit, it has large, glossy, dark seeds that are easily removed. When ripe, the skin is green and gives slightly to pressure, similar to the avocado.
When I bought them they were hard like golf balls. But left in the windowsill they have softened nicely over 3-4 days. I just cut in half and scooped out the flesh with a spoon. There are black seeds about the size of those in a watermelon. They are very sweet and do have certain banana-y richness, though I wouldn´t include strawberry or peach flavors. Some mango - maybe? Some sweet apple? The flesh, though soft and juicy, does have a certain fiberous quality, like a mango, but is also creamy. Very interesting. I could see it blended into something cold and tropical. Or maybe mixed in a salad with a soft brie. Some recipes here.
The orange globes are persimmons (hachiya, I believe, from the color).
Persimmons are eaten fresh, dried, raw, or cooked. When eaten fresh, the skin is usually cut/peeled off and the fruit is often cut into quarters or eaten whole like an apple. One way to consume very ripe persimmons, which can have the texture of pudding, is to remove the top leaf with a paring knife and scoop out the flesh with a spoon.
In the state of Indiana (USA), persimmons are harvested and used in a variety of dessert dishes most notably pies. It can be used in cookies, cakes, puddings, salads, curries  and as a topping for breakfast cereal. Persimmon pudding is a dessert using fresh persimmons. An annual persimmon festival, featuring a persimmon pudding contest, is held every September in Mitchell, Indiana. Persimmon pudding is a baked pudding that has the consistency of pumpkin pie but resembles a brownie and is almost always topped with whipped cream. Persimmons may be stored at room temperature (20 °C) where they will continue to ripen. In northern China, unripe persimmons are frozen outside during winter to speed up the ripening process.
One is softening but the other is still like a hockey puck after 3-4 days, so I´ll wait. Maybe I´ll try a persimmon pie.
1 recipe pastry for a 9 inch single crust pie
1/2 teaspoon ground cinnamon
1/2 cup white sugar
1/4 teaspoon salt
2 cups half-and-half cream
1 cup persimmon pulp
2 tablespoons butter, melted
1 teaspoon lemon juice
Preheat oven to 450 degrees F (230 degrees C).
Combine eggs, cinnamon, sugar, and salt. Mix in cream, persimmon pulp,
melted butter, and lemon juice. Pour into unbaked pie shell.
Bake for 10 minutes. Reduce heat to 350 degrees F (175 degrees C), and bake an
additional 30 minutes. Cool before slicing.