carlsen got to GM in 5-6 years. i got to NM in about 5 years.
From Carlsen's Wikipedia page "His father taught him to play chess at the age of 5..." and "Carlsen became a Grandmaster... at the age of 13 years..."
So it took him eight years. Slow coach 
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Candidate Master: This title is awarded to any player with an established FIDE rating of 2200 or higher. This is the least prestigious title awarded by FIDE.
I think womens fide titles that require even less than 2200 fide rating are less prestigious than CM title .
Getting a title in chess is really pointless. Even Kasparov has said on numerous occasions that chess is a big fat waste of time...!
So , why are you here wasting your time ? 
IM and GM are the original titles. FM and CM are mostly money grabs by FIDE, but ok, FM is a master title; it's more or less the equivalent of the "national master" title that some national federations give out.
But "candidate master" obviously means you're not a master yet, you're an officially recognized candidate to become one (which is silly, since there is no requirement to become a candidate before you become an actual master).
However, calling a CM a master is just wrong
Calling a CM master is not wrong. I am sure russian 2200 FIDE will be 2300+ USCF in USA. CM and NM most of the time are considered pretty equal. Infact if you are over 2200 fide, most likely you are already or pretty close to NM in your contry. And CM and FM titles i heard are paid by your country federation. CM means you are about to become FM, but still is master level player, but not all players, sometiems titles are given to low rated juniors or you can grab CM or FM if you play on zonals and score 50% no matter rating.
Possible - yes. Probable - no.
I've been playing chess for 20 years and I'm still only approx. 1750 on a very good day.
I think that you need to be naturally talented at chess to become a GM, although anyone can learn the game and become decent at it.
If you are about 6 years old, very talented, get systematic training and work hard, it is quite likely because of the plasticity of the brain. If you are older than 20 it is extremely unlikely (I would say chances are below 0.00001%). Of course, I have no evidence, but how many master strenght players can you name that started playing chess after the age of 20? I know only one, and he's is a fictional figure. Coincidence?
50 tactics a day.