Can one truly build a schedule from graph coloring?
[...] is this feasible in a real world scenario?


I'm not sure.  But note that determining the chromatic number of a graph and determining the minimum number of timeslots needed to schedule lectures with a given pattern of conflicts are exactly the same problem. So, if the scheduling problem can't be feasibly solved by colouring, it can't be feasibly solved any other way, either.


  Say I have 30 professors and 200 students, can we determine a minimum number of meeting times with a graph this size?


Note that the size of the graph depends only on the number of classes. The only effect that the number of students has is that having more students means there are more likely to be conflicts between more classes.


  And does the graph tell us when they need to meet?


No. It will just tell you "Here are sets $S_1, \dots, S_k$ that partition the classes."  All the classes in one set should be scheduled at the same time; different sets need to be at different times. The graph doesn't care whether you study algorithms at 10am and Java at 11am, or algorithms at 11 and Java at 10, or algorithms at 3am and Java at 3pm. All it knows is that, if at least one person is studying algorithms and Java, those two classes have to be at different times.


  In addition, could the graph take into account some lectures twice as long as other lectures?


Not directly.  But you could pretend that your two-hour electronics lab is really two one-hour labs called electronics1 and electronics2 which, of course, can't be at the same time, because students take both courses. And, because the graph doesn't care what time the classes are at, you can schedule electronics2 to be in the slot immediately after electronics1.