1. You would generally never use QR to compute eigenvectors.
2. EIG uses a different algorithm from the other tools, designed to solve a different problem. Various algorithms take varying amounts of time, dependent on the problem.
3. You CAN use svd to compute eigenvectors for specific problems. SVD can sometimes be more or less time consuming than EIG. (Usually slower, but I can probably give an example where SVD is faster.)
4. Take a numerical linear algebra course, explaining all of the above. Or read some of the multiple books out there on the subject.
