Advice needed I 10 years

Came to the uk in 2004 legally on a Working holiday visa.
2006 switch to student visa until 2011.
2011 I did a civil partnership
Civil partnerships broke down last year in 2013.
Civil partnership not been dissolved yet.
My option now is to apply for the IT in The UK
Not left the country for more than 9 days in this 10 years.

I have passed my Life in UK test last week.
I'm writing the Esol level 3 Grade 5 in two weeks time.I was advised the home office accept this level for the English test required test.Is this correct?

one more question.How long does it take to be approved?.

If I do the on the day application, is that the best way to go about,

Yes time as an EEA family member can be included for SET(LR) however, you'll have to show your partner was exercising treaty rights, if he was?