If I am getting this right, we are supposed to use SEB to attend quiz.
Is there a way to launch SEB from another browser (e.g. IE or FF) when starting quiz and exit automatically when submitting answers?
See our roadmap (but please consider: since we might extend the project by 4 months, the timings in the roadmap will most likely change): http://www.safeexambrowser.org/about_roadmap_en.html
Yes, we plan to implement automatic quitting in SEB after the exam was submitted. But this requires also changes/extensions in the LMS used, we are discussing this with the Moodle and ILIAS guys.
There also will be a way to start SEB from another browser, even with an individual configuration per quiz, using new encrypted .seb configuration files. This is not mentioned in the roadmap, but we are working on that right now.