Questions for EEA Family Permit

[tusea1]

Hello, my name is Denis, here is my situation
i am Ukrainian(non EU)
my wife is Romanian(EU National)
currently we live in Greece(i am undergraduate student and she is unemployed)

i have applied for postgraduate courses to some uni in UK and have got already many offers for September 2015

So we plan to move in UK next September, and i think the EEA family permit route
will be better that the Student Visa, so here are my questions:

1.will i be able to enroll at the university as a holder of a EEA family permit that is valid only for six months(less than the duration of my course that will be for 1 year)?

2.i know that within 6 months of the EEA Family Permit i will be able to apply for Resident Permit for 5 years, but will this be possible in my ocassion supposing that
i will be a student and my wife will be unemployed/jobseeker in UK?

3.and the finally ,supposing that the answer for the second question is YES,when i will apply for Permit Residence how should i prove that she is a jobseeker?

Thank you !