Some universities certainly do have a reputation for developing NFL players. In some cases, this is simply due to quality of the program - Alabama for example is a very good program and as such attracts very good players; this not only means a player will play alongside other good players (and thus learn better habits/etc.), but also means a player will be exposed more on national TV and to scouts.
NFL team scouts only can go to limited numbers of games, and while they can undoubtedly watch many more on taped broadcasts, there's something different about going to a game; even relatively un-heralded players can be seen performing well in a game. This means teams like USC, Notre Dame, etc., give players more of a chance to get on TV and be discovered by scouts, leading to them getting better players than they otherwise would. This may not correlate to NFL success, but it tends to correlate with numbers.
Some coaches also have a good reputation for developing certain kinds of players. Steve Spurrier had a reputation for developing quarterbacks while at Florida, although most of his eventually fizzled out (at which point people realized it was the 'system').
I would note that in both of these cases, I mean 'reputation' as in it is thought that these teams/coaches are skilled; Spurrier is a great example of where that reputation was misguided, as none of his QBs really panned out (Rex Grossman is probably the best of the lot in terms of NFL career, and, well, I'm a Bears fan, so you probably know how I feel about that.)
Finally, some schools or even conferences have reputations for certain types of players. The Big 10, and particularly Wisconsin, OSU, and (until recently) Michigan, had a reputation for developing offensive linemen; a high proportion of NFL linemen, both stars and solid but mostly unknown starters, came from the big 10 (or at least, did; some of this reputation may be less deserved now than it was).
Success in NCAA and success in NFL are less tightly connected then, say, success in the NBA vs NCAA. Football is a very physical sport, and players in college are still often not fully developed. They also have a large learning curve still in the NFL. Connecting this to the draft questions, while early draft round is correlated to success, it's not tightly correlated, except in a few positions (QB, in particular), and it tends to be more that good players are drafted in the early rounds - but not nearly all early round draftees are good players. You can look online for some details of this; for example, a ten year draft study showed that almost half of first round players were 'busts'.
As to why QB correlates better, it is a combination of things. This is only true of 'NFL style' offenses, though that may be in the process of changing some with the NFL read option (if that sticks); ie, colleges who use a pocket passer and run neither an option nor a spread offense.
For those colleges who do run NFL style offenses, a quarterback is easier to evaluate because his skill is directly visible (you see him throw the ball, see him make decisions, etc.) more readily than some other players. It's more obvious when he makes mistakes. The offense is centered around him to some extent, and his ability to learn and understand is very obvious from the game play.
Quarterback is also a position teams realize (in the NFL) that is very important, and as such they do a lot more scouting, a lot more research and interviews, and most importantly are willing to take chances on QB more so than on other players. You will always have someone fall through the cracks - the undrafted Tony Romo or the sixth round Tom Brady - but particularly in the last decade or so it's been well understood that in the salary cap era, particularly with (limited) rookie scale salaries, having a reasonably cheap, good quarterback is very important to success (see Seattle and San Francisco for great recent examples of building a team with a cheap QB). This isn't to say you still have mistakes - Russell Wilson made it to the middle of the third round, for example - but those are usually due to assumptions of physical deficiencies (in his case, height) that usually correspond to low success rates.
I would say that Wide Receiver is the second easiest to guess, in large part because the potential true superstars are due to physical elements (height and weight, and speed). Calvin Johnson and AJ Green are very obvious physical specimens who were clearly stars coming out of college. On the other hand, the star WR from the last draft class was Odell Beckham, who was drafted fifth out of the (very deep) WR class. WRs who aren't physical specimens are hard to separate from their team and the opposing defenses: is a WR who sprints downfield and catches touchdowns just better than mediocre CBs, or has a QB who throws the ball in just the right place? Or is it his personal skill? It's difficult to separate those things, so it's hard to say how good the WR is. QBs throw to several different receivers, so at least that can be teased out some; the WR is likely to only have one QB throwing to him, unless he plays for Ohio State.
