Can the Flash do things like build muscle faster than normal (do his muscles grow right after a work-out or meal)? Can he heal faster than normal? Does he have a faster immune system to stop all illness or at least make the flu last 2 minutes or something along those lines?
As with almost anything related to superheroes, this has been inconsistently portrayed throught the history of the character.
First, we must consider which Flash you are talking about. It also depends on several other factors, notably which version of the character (mainstream comics, New 52, parallel universes, the TV show, the DCAU, etc).
To boil it down, the answer is generally yes, The Flash does do every bodily process faster than a normal human being. How much faster varies (sometimes within the same story!) as does how much control he has over it.
Generally, every version of The Flash heals faster than a normal human (though not so fast as, say, Wolverine). Bruises will be gone within a day or so, cuts and stuff will heal faster, cracked ribs will knit quicker, etc. His body processes toxins at an increased rate, which means he'd have a heck of a time getting drunk and things like drugs and knockout gasses can wear off sooner. That said, he still breathes (most of the time) at a normal human rate, and he can get sick.
Most writers generally explain this as a factor of his powers: his Super Speed isn't always on. He doesn't always move faster than everyone else, and he doesn't always perceive things the way he does when he's moving faster than the speed of sound. His body, by default, is not going that much faster than everyone else is. It does, however, speed up as he does. So if he and Batman are talking when giant metal panels shut them in a room and it fills with knockout gas, Batman will likely wake up first (due to his better constitution and higher body mass) - Flash wasn't going at super speed, so his body wasn't accelerating his metabolic processes.
That said, Flash has never shown any propensity for increased speed at building muscle mass. His physical strength is normal for a fit man of his build. He can bench his own weight and has been shown to be able to carry one or two people at a time.
The Flash can, however, read incredibly fast. Barry Allen and Wally West can read libraries in seconds, though what they learn from those books fades quickly, so it's typically used to find one or two relevant facts (which they then tell to others). Bart Allen, on the other hand, possesses a photographic memory and can (and has) read libraries and retained all the information.