I assume your confusion comes from failing to distinguish two different words spelled to.
The examples in your question aren't exceptions. They contain the preposition to:
The key [ to being more productive ] is ...
I look forward [ to seeing you ].
He admitted [ to taking the money ].
Scientists are closer [ to being able to ... ].
seven steps [ to reaching your goals ]
In each case, the -ing form of the verb is what is traditionally called a gerund. When the verb is in its gerund form, the clause as a whole functions very much like a noun phrase.
Each of the bracketed phrases is a preposition phrase.
This should be distinguished from the infinitive marker to:
I want [ to eat as many sandwiches as possible ].
I'd like [ to visit New York ].
In each of these examples, the bracketed portion is a to-infinitival clause.
The word to in these examples marks the clause as infinitive; the -ing form is not possible here.
The very short answer: they do it just the same way that you learned all that difficult grammar in your own mother tongue.
Slightly longer:
How does anyone learn their native language?
Well, according to linguists, they do not.
The process of getting to know how to speak your mother tongue is called acquisition, not learning.
Learning is what other people do when they learn the language as a second (or third, etc) language. They learn the rules, the grammar, and they try to apply them.
Young children subconsciously analyse the words and phrases they hear around them, and they build up a "grammar" in their head, as well as a dictionary, a thesaurus, enormous lists of collocations, etc. They don't actually sit down to study, they just absorb and analyse.
So a native speaker knows that he should say he works instead of he work, and even when he encounters a verb that he has never seen before, he knows the third person singular will get an -s in the simple present.
The amazing thing is that he knows that, even if maybe he does not know anything about grammar. Even if he doesn't know what a "verb" is, what "simple present is", or "third person singular". Even if he has never seen a grammar book, he will be able to correctly say he (new verb)s.
Just look around you at any young kids. You may think that your mother tongue is easy, because even little children speak it very well. But it's not. It's as easy or difficult as English is, and those kids (and you, when you were little) are doing what children everywhere do: they build up an understanding of the grammar of their mother tongue without even realizing it.
Ask a five-year old why he just conjugated that verb correctly, ask him in which grammar book he saw the rules for that, and at best you will get a blank stare.
You had discovered an enormous amount of grammar by the age of three, just like any kid, in any language.
This question reminds me of this old joke:
I am so glad I was not born in China, because I don't speak a word of Chinese!
Best Answer
What is that key for? is correct. It's what people say and write. The other two examples are not constructed as English speakers would say them. In fact, the second one is quite wrong. The third one might once have been considered correct as there is a misguided perception that sentences should not end with a preposition. From The Chicago Manual of Style Online 5.180:
I have not included a link, as CMOS is behind a paywall.