Nobody answered your questions, because things are done differently at different studios.
1)
Effects usually created by computer scientists, animators or pyrotechnicians, maybe a combination of all of them, depending on the effect. Not Compositors.
An example is the Perfect Storm, ILM had computer scientists create a program to model waves using math i can't begin to understand.
While holgraphic interfaces like in Final Fantasy where done by 3d Animators.
Things like flames can be created in many different ways, either cg or a pyrotechnics.
The explosion for the matrix truck scene was no doubt a combination of 3d animators and computer engineers.
So the effects created depends on what it is and what techniques and skills are needed for those effects.
Compositors(Compers) just usually put things together but they also have to match things like lighting, fake shadows, color correcting, reflections and have to know many other things. Usually they don't create those things.
Maybe the closest a compositor got to creating effects was that scene in Lord of the Rings Two Towers when Frodo fell in that marsh with dead ghost people in it. Not sure if that was done in compositing though.
2)really really depends where you go and what responsibilities your job has. One place could be a sweat shop while another could be like disneyland. One thing is for sure though, you will be working very hard to meet your deadlines.
3)??? Try buying or looking for an issue of Cinefex. You will see what kind of work goes to Different Effects. Usually Computer Scientists consulting with Physicists and Engineers do those effects.
4)It really depends on what the Compositors Know how to do and if they qualify for an different role. There are many different types of TD's specializing in different areas, but they typically know how to get things to work. A vfx supervisor must know how to manage everything and plan how a shot will be created.
5)Usually at larger places you are assigned to a department and stick to your role, the pipeline runs smoothly that way. Smaller studios tend to have more jacks of all trades.
6)Compositors usually try to make things look realistic and match things up, such as matching color and shadows. It is more technical than creative.
So compositors just integrate things together. Hope that helps