As far as when a TB stops growing, it's the same as any other horse, usually they are mature at age 5-6... there arent really any drugs to make them run faster, but steroids are used to help build muscle mass, lasix is used to help prevent pulmonary hemmorage, and anti inflamitory drugs (NSAID's) to help reduce inflamation and pain... Lasix and some NSAID's are legal in small dosages... steroid use is on it's way to be being banned, and already is in some states.
Of course your going to have trainers push the envelope with drugs, but it's the same in almost all diciplines if you look hard enough.
One thing to keep in mind is that management of horses comes in different forms, there are good trainers and there are bad trainers, as well as good trainers and good horses that have terrible things happen to them.
Eight Belles had never been given steroids, no illegal drugs were found in her system and was xrayed clean with no apparent injuries before she broke down in the Derby. That being said, there are plenty of TB's that race as two yr olds and never break down, and go on to have productive careers as racehorses.
Thank you all for your opinions and suggests and thanks to covekat who provided me with a quote!