Learn English – After request vs after a request

You are right that it gets a little confusing with things like mountains, rivers, etc.

I was going to type up some examples, but this site does it just fine. To summarize it (including only ones relevant to this question):

without "the"

• names of countries in the singular; summits of mountains; continents; towns
• single islands
• parks; lakes

With "the"

• names of countries in the plural; mountain ranges; regions
• groups of islands
• name with of-phrase (ex: The Statue of Liberty); oceans; seas; rivers

I wish I could give you an easy rule to follow with this... but I cant. Some things just work one way, and others a different way. Maybe an expert could explain why the distinction was made. I guess, eventually, you just develop an ear for it. Until then, you may have to just memorize the common examples, and try to use that to "guess" for the other ones.

The "zero article", otherwise known as simply not using an article, either indicates a proper name, or an abstract concept.

Apple is the most common fruit in the region.

This cannot be correct, because you are not talking about the abstract concept of an apple, but rather about a very real and concrete object.

Apple is the platonic ideal of fruit.

This example is closer to correct, because we are now talking about the concept of the apple, but even here, apple is simple to real and concrete to be usable with the zero article. This is also wrong.

Apple is on my mind.

Finally, we have come to a correct sentence, thoroughly converting a concrete noun into an abstract concept that I am merely thinking about. But even here, alone, without context, the idea of treating the word "apple" as an abstract concept is so strange that most people would reinterpret the sentence to treat "Apple" as a proper noun instead, especially since there exists a very real and well known company with the proper name of "Apple". But it does work, grammatically, the other way... it's just a very strange idea. You might find it in a philosophy textbook.