For what it is worth:
I applied for an SGPO position with TVA in Dec 2006, took the EEI in Feb 2007, interviewed for the position in May 2007, graduated from college in June 2007 and hired in Aug 2007. Maybe that gives you an idea of the time frame involved, the times can obviously vary on a case by case basis.
Regarding your third question, Bradtv gives some good advice. I have solid information that a few of the guys that did interview at the same time as me, but were not hired, did get picked up for subsequent SGPO classes. So don't give up!
Take heart; if you did pass the EEI exam at the nuclear operator level you've already cleared one of the most difficult hurdles. We lose most applicants at this stage of the process.
Good luck!