I started looking into the history of a few grandmasters such as Fischer and Carlsen, so I wondered: why does it seem that chess "kings" and queens" start playing the game from a young age? Can anyone show me any grandmasters who started playing chess after becoming 18? Does this situation apply to other things such as physical sports or even more mental-focused skills such as doing math?
In pretty much any endeavor that requires one to develop or acquire complex sets of skills, be it chiefly intellectual or chiefly physical, starting young will generally be a huge boon simply because of the fact that younger brains are more plastic than older brains; they can more readily adapt to new sorts of tasks and information. Because of that fact, chess will be no different from sports or math or whatever, and those who rise to the very top will tend to have started quite young, as that makes much easier the ultimate task of acquiring the specialized knowledge and skills that are necessary in order to play chess with the very best. Even so, some remarkably strong players have indeed gotten relatively late starts.
Mikhail Chigorin first learned the rules of chess at the fairly late age of 16, and didn't really throw himself into chess until he was already 23-24. A quote from Wikipedia:
He became serious about chess uncommonly late in life; his schoolteacher taught him the moves at the age of 16, but he did not take to the game until around 1874, having first finished his studies before commencing a career as a government officer.
All in all, I think Chigorin thus reasonably meets your criterion of having started after age 18. Technically, he was not a "grandmaster" in the sense of having that official FIDE title, but of course that's only because it didn't exist in Chigorin's day. He played two matches for Steinitz's world championship, and chessmetrics places Chigorin in the world's top 4 players throughout the 1890s (peaking at #2 behind Steinitz and Lasker at different times).
In addition, Howard Staunton apparently started playing chess only at age 26. Like Chigorin, he of course was not technically a GM in the modern sense of the word, but he is generally recognized as having been the strongest player in the world the 1840s, and is sometimes referred to as an "unofficial world champion" the way that Paul Morphy often is.
Wilhelm Steinitz learned "how" to play chess at the age of 12, but it was only after attending the Vienna Polytechnic that he actually began to play serious chess (sometime during his twenties).
Siegbert Tarrasch learned how to play chess when he was 15, but he was 20 when he first tried himself at a "Hauptturneier" (Chess Tournament) in 1882 at Berlin, he was eliminated from the tournament.
There should be more examples, but these two never really took chess serious before reaching their 20's, Siegbert Tarrasch was actually attending University of Halle-Wittenberg and at the beginning of his profession as a medical doctor he actually put chess in second place after his medical practice.